2.4.8.1. ERKStep User-callable functions

This section describes the ERKStep-specific functions that may be called by the user to setup and then solve an IVP using the ERKStep time-stepping module. The large majority of these routines merely wrap underlying ARKODE functions, and are now deprecated – each of these are clearly marked. However, some of these user-callable functions are specific to ERKStep, as explained below.

As discussed in the main ARKODE user-callable function introduction, each of ARKODE’s time-stepping modules clarifies the categories of user-callable functions that it supports. ERKStep supports the following categories:

temporal adaptivity
relaxation Runge–Kutta methods

ERKStep also has forcing function support when converted to a SUNStepper or MRIStepInnerStepper. See ARKodeCreateSUNStepper() and ARKStepCreateMRIStepInnerStepper() for additional details.

2.4.8.1.1. ERKStep initialization and deallocation functions

void *ERKStepCreate(ARKRhsFn f, sunrealtype t0, N_Vector y0, SUNContext sunctx)

This function allocates and initializes memory for a problem to be solved using the ERKStep time-stepping module in ARKODE.

Arguments:

f – the name of the C function (of type ARKRhsFn()) defining the right-hand side function in \(\dot{y} = f(t,y)\).
t0 – the initial value of \(t\).
y0 – the initial condition vector \(y(t_0)\).
sunctx – the SUNContext object (see §1.3)

Return value:

If successful, a pointer to initialized problem memory of type void*, to be passed to all user-facing ERKStep routines listed below. If unsuccessful, a NULL pointer will be returned, and an error message will be printed to stderr.

void ERKStepFree(void **arkode_mem)

This function frees the problem memory arkode_mem created by ERKStepCreate().

Arguments:

arkode_mem – pointer to the ERKStep memory block.

Return value: None

Deprecated since version 6.1.0: Use ARKodeFree() instead.

2.4.8.1.2. ERKStep tolerance specification functions

int ERKStepSStolerances(void *arkode_mem, sunrealtype reltol, sunrealtype abstol)

This function specifies scalar relative and absolute tolerances.

Arguments:

arkode_mem – pointer to the ERKStep memory block.
reltol – scalar relative tolerance.
abstol – scalar absolute tolerance.

Return value:

ARK_SUCCESS if successful
ARK_MEM_NULL if the ERKStep memory was NULL
ARK_NO_MALLOC if the ERKStep memory was not allocated by the time-stepping module
ARK_ILL_INPUT if an argument had an illegal value (e.g. a negative tolerance).

Deprecated since version 6.1.0: Use ARKodeSStolerances() instead.

int ERKStepSVtolerances(void *arkode_mem, sunrealtype reltol, N_Vector abstol)

This function specifies a scalar relative tolerance and a vector absolute tolerance (a potentially different absolute tolerance for each vector component).

Arguments:

arkode_mem – pointer to the ERKStep memory block.
reltol – scalar relative tolerance.
abstol – vector containing the absolute tolerances for each solution component.

Return value:

ARK_SUCCESS if successful
ARK_MEM_NULL if the ERKStep memory was NULL
ARK_NO_MALLOC if the ERKStep memory was not allocated by the time-stepping module
ARK_ILL_INPUT if an argument had an illegal value (e.g. a negative tolerance).

Deprecated since version 6.1.0: Use ARKodeSVtolerances() instead.

int ERKStepWFtolerances(void *arkode_mem, ARKEwtFn efun)

This function specifies a user-supplied function efun to compute the error weight vector ewt.

Arguments:

arkode_mem – pointer to the ERKStep memory block.
efun – the name of the function (of type ARKEwtFn()) that implements the error weight vector computation.

Return value:

ARK_SUCCESS if successful
ARK_MEM_NULL if the ERKStep memory was NULL
ARK_NO_MALLOC if the ERKStep memory was not allocated by the time-stepping module

Deprecated since version 6.1.0: Use ARKodeWFtolerances() instead.

2.4.8.1.3. Rootfinding initialization function

int ERKStepRootInit(void *arkode_mem, int nrtfn, ARKRootFn g)

Initializes a rootfinding problem to be solved during the integration of the ODE system. It must be called after ERKStepCreate(), and before ERKStepEvolve().

Arguments:

arkode_mem – pointer to the ERKStep memory block.
nrtfn – number of functions \(g_i\), an integer \(\ge\) 0.
g – name of user-supplied function, of type ARKRootFn(), defining the functions \(g_i\) whose roots are sought.

Return value:

ARK_SUCCESS if successful
ARK_MEM_NULL if the ERKStep memory was NULL
ARK_MEM_FAIL if there was a memory allocation failure
ARK_ILL_INPUT if nrtfn is greater than zero but g = NULL.

Notes:

To disable the rootfinding feature after it has already been initialized, or to free memory associated with ERKStep’s rootfinding module, call ERKStepRootInit with nrtfn = 0.

Similarly, if a new IVP is to be solved with a call to ERKStepReInit(), where the new IVP has no rootfinding problem but the prior one did, then call ERKStepRootInit with nrtfn = 0.

Deprecated since version 6.1.0: Use ARKodeRootInit() instead.

2.4.8.1.4. ERKStep solver function

int ERKStepEvolve(void *arkode_mem, sunrealtype tout, N_Vector yout, sunrealtype *tret, int itask)

Integrates the ODE over an interval in \(t\).

Arguments:

arkode_mem – pointer to the ERKStep memory block.
tout – the next time at which a computed solution is desired.
yout – the computed solution vector.
tret – the time corresponding to yout (output).
itask – a flag indicating the job of the solver for the next user step.

The ARK_NORMAL option causes the solver to take internal steps until it has just overtaken a user-specified output time, tout, in the direction of integration, i.e. \(t_{n-1} <\) tout \(\le t_{n}\) for forward integration, or \(t_{n} \le\) tout \(< t_{n-1}\) for backward integration. It will then compute an approximation to the solution \(y(tout)\) by interpolation (using one of the dense output routines described in §2.2.2).

The ARK_ONE_STEP option tells the solver to only take a single internal step, \(y_{n-1} \to y_{n}\), and return the solution at that point, \(y_{n}\), in the vector yout.

Return value:

ARK_SUCCESS if successful.
ARK_ROOT_RETURN if ERKStepEvolve() succeeded, and found one or more roots. If the number of root functions, nrtfn, is greater than 1, call ERKStepGetRootInfo() to see which \(g_i\) were found to have a root at (*tret).
ARK_TSTOP_RETURN if ERKStepEvolve() succeeded and returned at tstop.
ARK_MEM_NULL if the arkode_mem argument was NULL.
ARK_NO_MALLOC if arkode_mem was not allocated.
ARK_ILL_INPUT if one of the inputs to ERKStepEvolve() is illegal, or some other input to the solver was either illegal or missing. Details will be provided in the error message. Typical causes of this failure:
1. A component of the error weight vector became zero during internal time-stepping.
2. A root of one of the root functions was found both at a point \(t\) and also very near \(t\).
3. The initial condition violates the inequality constraints.
ARK_TOO_MUCH_WORK if the solver took mxstep internal steps but could not reach tout. The default value for mxstep is MXSTEP_DEFAULT = 500.
ARK_TOO_MUCH_ACC if the solver could not satisfy the accuracy demanded by the user for some internal step.
ARK_ERR_FAILURE if error test failures occurred either too many times (ark_maxnef) during one internal time step or occurred with \(|h| = h_{min}\).
ARK_VECTOROP_ERR a vector operation error occurred.

Notes:

The input vector yout can use the same memory as the vector y0 of initial conditions that was passed to ERKStepCreate().

In ARK_ONE_STEP mode, tout is used only on the first call, and only to get the direction and a rough scale of the independent variable.

All failure return values are negative and so testing the return argument for negative values will trap all ERKStepEvolve() failures.

Since interpolation may reduce the accuracy in the reported solution, if full method accuracy is desired the user should issue a call to ERKStepSetStopTime() before the call to ERKStepEvolve() to specify a fixed stop time to end the time step and return to the user. Upon return from ERKStepEvolve(), a copy of the internal solution \(y_{n}\) will be returned in the vector yout. Once the integrator returns at a tstop time, any future testing for tstop is disabled (and can be re-enabled only though a new call to ERKStepSetStopTime()).

On any error return in which one or more internal steps were taken by ERKStepEvolve(), the returned values of tret and yout correspond to the farthest point reached in the integration. On all other error returns, tret and yout are left unchanged from those provided to the routine.

Deprecated since version 6.1.0: Use ARKodeEvolve() instead.

2.4.8.1.5. Optional input functions

2.4.8.1.5.1. Optional inputs for ERKStep

int ERKStepSetDefaults(void *arkode_mem)

Resets all optional input parameters to ERKStep’s original default values.

Arguments:

arkode_mem – pointer to the ERKStep memory block.

Return value:

ARK_SUCCESS if successful
ARK_MEM_NULL if the ERKStep memory is NULL
ARK_ILL_INPUT if an argument had an illegal value

Notes:

Does not change problem-defining function pointer f or the user_data pointer.

Also leaves alone any data structures or options related to root-finding (those can be reset using ERKStepRootInit()).

Deprecated since version 6.1.0: Use ARKodeSetDefaults() instead.

int ERKStepSetInterpolantType(void *arkode_mem, int itype): Deprecated since version 6.1.0: This function is now a wrapper to ARKodeSetInterpolantType(), see the documentation for that function instead.

int ERKStepSetInterpolantDegree(void *arkode_mem, int degree)

Specifies the degree of the polynomial interpolant used for dense output (i.e. interpolation of solution output values and implicit method predictors).

Arguments:

arkode_mem – pointer to the ERKStep memory block.
degree – requested polynomial degree.

Return value:

ARK_SUCCESS if successful
ARK_MEM_NULL if the ERKStep memory or interpolation module are NULL
ARK_INTERP_FAIL if this is called after ERKStepEvolve()
ARK_ILL_INPUT if an argument had an illegal value or the interpolation module has already been initialized

Notes:

Allowed values are between 0 and 5.

This routine should be called after ERKStepCreate() and before ERKStepEvolve(). After the first call to ERKStepEvolve() the interpolation degree may not be changed without first calling ERKStepReInit().

If a user calls both this routine and ERKStepSetInterpolantType(), then ERKStepSetInterpolantType() must be called first.

Since the accuracy of any polynomial interpolant is limited by the accuracy of the time-step solutions on which it is based, the actual polynomial degree that is used by ERKStep will be the minimum of \(q-1\) and the input degree, for \(q > 1\) where \(q\) is the order of accuracy for the time integration method.

Changed in version 5.5.1: When \(q=1\), a linear interpolant is the default to ensure values obtained by the integrator are returned at the ends of the time interval.

Deprecated since version 6.1.0: Use ARKodeSetInterpolantDegree() instead.

int ERKStepSetDenseOrder(void *arkode_mem, int dord): Deprecated since version 5.2.0: Use ARKodeSetInterpolantDegree() instead.

int ERKStepSetDiagnostics(void *arkode_mem, FILE *diagfp)

Specifies the file pointer for a diagnostics file where all ERKStep step adaptivity and solver information is written.

Arguments:

arkode_mem – pointer to the ERKStep memory block.
diagfp – pointer to the diagnostics output file.

Return value:

ARK_SUCCESS if successful
ARK_MEM_NULL if the ERKStep memory is NULL
ARK_ILL_INPUT if an argument had an illegal value

Notes:

This parameter can be stdout or stderr, although the suggested approach is to specify a pointer to a unique file opened by the user and returned by fopen. If not called, or if called with a NULL file pointer, all diagnostics output is disabled.

When run in parallel, only one process should set a non-NULL value for this pointer, since statistics from all processes would be identical.

Deprecated since version 5.2.0: Use SUNLogger_SetInfoFilename() instead.

int ERKStepSetFixedStep(void *arkode_mem, sunrealtype hfixed)

Disabled time step adaptivity within ERKStep, and specifies the fixed time step size to use for the following internal step(s).

Arguments:

arkode_mem – pointer to the ERKStep memory block.
hfixed – value of the fixed step size to use.

Return value:

ARK_SUCCESS if successful
ARK_MEM_NULL if the ERKStep memory is NULL
ARK_ILL_INPUT if an argument had an illegal value

Notes:

Pass 0.0 to return ERKStep to the default (adaptive-step) mode.

Use of this function is not generally recommended, since we it gives no assurance of the validity of the computed solutions. It is primarily provided for code-to-code verification testing purposes.

When using ERKStepSetFixedStep(), any values provided to the functions ERKStepSetInitStep(), ERKStepSetAdaptivityFn(), ERKStepSetMaxErrTestFails(), ERKStepSetAdaptivityMethod(), ERKStepSetCFLFraction(), ERKStepSetErrorBias(), ERKStepSetFixedStepBounds(), ERKStepSetMaxEFailGrowth(), ERKStepSetMaxFirstGrowth(), ERKStepSetMaxGrowth(), ERKStepSetMinReduction(), ERKStepSetSafetyFactor(), ERKStepSetSmallNumEFails(), ERKStepSetStabilityFn(), and ERKStepSetAdaptController() will be ignored, since temporal adaptivity is disabled.

If both ERKStepSetFixedStep() and ERKStepSetStopTime() are used, then the fixed step size will be used for all steps until the final step preceding the provided stop time (which may be shorter). To resume use of the previous fixed step size, another call to ERKStepSetFixedStep() must be made prior to calling ERKStepEvolve() to resume integration.

It is not recommended that ERKStepSetFixedStep() be used in concert with ERKStepSetMaxStep() or ERKStepSetMinStep(), since at best those latter two routines will provide no useful information to the solver, and at worst they may interfere with the desired fixed step size.

Deprecated since version 6.1.0: Use ARKodeSetFixedStep() instead.

int ERKStepSetInitStep(void *arkode_mem, sunrealtype hin)

Specifies the initial time step size ERKStep should use after initialization, re-initialization, or resetting.

Arguments:

arkode_mem – pointer to the ERKStep memory block.
hin – value of the initial step to be attempted \((\ne 0)\).

Return value:

ARK_SUCCESS if successful
ARK_MEM_NULL if the ERKStep memory is NULL
ARK_ILL_INPUT if an argument had an illegal value

Notes:

Pass 0.0 to use the default value.

By default, ERKStep estimates the initial step size to be \(h = \sqrt{\dfrac{2}{\left\| \ddot{y} \right\|}}\), where \(\ddot{y}\) is an estimate of the second derivative of the solution at \(t_0\).

This routine will also reset the step size and error history.

Deprecated since version 6.1.0: Use ARKodeSetInitStep() instead.

int ERKStepSetMaxHnilWarns(void *arkode_mem, int mxhnil)

Specifies the maximum number of messages issued by the solver to warn that \(t+h=t\) on the next internal step, before ERKStep will instead return with an error.

Arguments:

arkode_mem – pointer to the ERKStep memory block.
mxhnil – maximum allowed number of warning messages \((>0)\).

Return value:

ARK_SUCCESS if successful
ARK_MEM_NULL if the ERKStep memory is NULL
ARK_ILL_INPUT if an argument had an illegal value

Notes:

The default value is 10; set mxhnil to zero to specify this default.

A negative value indicates that no warning messages should be issued.

Deprecated since version 6.1.0: Use ARKodeSetMaxHnilWarns() instead.

int ERKStepSetMaxNumSteps(void *arkode_mem, long int mxsteps)

Specifies the maximum number of steps to be taken by the solver in its attempt to reach the next output time, before ERKStep will return with an error.

Arguments:

arkode_mem – pointer to the ERKStep memory block.
mxsteps – maximum allowed number of internal steps.

Return value:

ARK_SUCCESS if successful
ARK_MEM_NULL if the ERKStep memory is NULL
ARK_ILL_INPUT if an argument had an illegal value

Notes:

Passing mxsteps = 0 results in ERKStep using the default value (500).

Passing mxsteps < 0 disables the test (not recommended).

Deprecated since version 6.1.0: Use ARKodeSetMaxNumSteps() instead.

int ERKStepSetMaxStep(void *arkode_mem, sunrealtype hmax)

Specifies the upper bound on the magnitude of the time step size.

Arguments:

arkode_mem – pointer to the ERKStep memory block.
hmax – maximum absolute value of the time step size \((\ge 0)\).

Return value:

ARK_SUCCESS if successful
ARK_MEM_NULL if the ERKStep memory is NULL
ARK_ILL_INPUT if an argument had an illegal value

Notes:

Pass hmax \(\le 0.0\) to set the default value of \(\infty\).

Deprecated since version 6.1.0: Use ARKodeSetMaxStep() instead.

int ERKStepSetMinStep(void *arkode_mem, sunrealtype hmin)

Specifies the lower bound on the magnitude of the time step size.

Arguments:

arkode_mem – pointer to the ERKStep memory block.
hmin – minimum absolute value of the time step size \((\ge 0)\).

Return value:

ARK_SUCCESS if successful
ARK_MEM_NULL if the ERKStep memory is NULL
ARK_ILL_INPUT if an argument had an illegal value

Notes:

Pass hmin \(\le 0.0\) to set the default value of 0.

Deprecated since version 6.1.0: Use ARKodeSetMinStep() instead.

int ERKStepSetStopTime(void *arkode_mem, sunrealtype tstop)

Specifies the value of the independent variable \(t\) past which the solution is not to proceed.

Arguments:

arkode_mem – pointer to the ERKStep memory block.
tstop – stopping time for the integrator.

Return value:

ARK_SUCCESS if successful
ARK_MEM_NULL if the ERKStep memory is NULL
ARK_ILL_INPUT if an argument had an illegal value

Notes:

The default is that no stop time is imposed.

Once the integrator returns at a stop time, any future testing for tstop is disabled (and can be re-enabled only though a new call to ERKStepSetStopTime()).

A stop time not reached before a call to ERKStepReInit() or ERKStepReset() will remain active but can be disabled by calling ERKStepClearStopTime().

Deprecated since version 6.1.0: Use ARKodeSetStopTime() instead.

int ERKStepSetInterpolateStopTime(void *arkode_mem, sunbooleantype interp)

Specifies that the output solution should be interpolated when the current \(t\) equals the specified tstop (instead of merely copying the internal solution \(y_n\)).

Arguments:

arkode_mem – pointer to the ERKStep memory block.
interp – flag indicating to use interpolation (1) or copy (0).

Return value:

ARK_SUCCESS if successful
ARK_MEM_NULL if the ERKStep memory is NULL

Added in version 5.6.0.

Deprecated since version 6.1.0: Use ARKodeSetInterpolateStopTime() instead.

int ERKStepClearStopTime(void *arkode_mem)

Disables the stop time set with ERKStepSetStopTime().

Arguments:

arkode_mem – pointer to the ERKStep memory block.

Return value:

ARK_SUCCESS if successful
ARK_MEM_NULL if the ERKStep memory is NULL

Notes:

The stop time can be re-enabled though a new call to ERKStepSetStopTime().

Added in version 5.5.1.

Deprecated since version 6.1.0: Use ARKodeClearStopTime() instead.

int ERKStepSetUserData(void *arkode_mem, void *user_data)

Specifies the user data block user_data and attaches it to the main ERKStep memory block.

Arguments:

arkode_mem – pointer to the ERKStep memory block.
user_data – pointer to the user data.

Return value:

ARK_SUCCESS if successful
ARK_MEM_NULL if the ERKStep memory is NULL
ARK_ILL_INPUT if an argument had an illegal value

Notes:

If specified, the pointer to user_data is passed to all user-supplied functions for which it is an argument; otherwise NULL is passed.

Deprecated since version 6.1.0: Use ARKodeSetUserData() instead.

int ERKStepSetMaxErrTestFails(void *arkode_mem, int maxnef)

Specifies the maximum number of error test failures permitted in attempting one step, before returning with an error.

Arguments:

arkode_mem – pointer to the ERKStep memory block.
maxnef – maximum allowed number of error test failures \((>0)\).

Return value:

ARK_SUCCESS if successful
ARK_MEM_NULL if the ERKStep memory is NULL
ARK_ILL_INPUT if an argument had an illegal value

Notes:

The default value is 7; set maxnef \(\le 0\) to specify this default.

Deprecated since version 6.1.0: Use ARKodeSetMaxErrTestFails() instead.

int ERKStepSetConstraints(void *arkode_mem, N_Vector constraints)

Specifies a vector defining inequality constraints for each component of the solution vector \(y\).

Arguments:

arkode_mem – pointer to the ERKStep memory block.
constraints – vector of constraint flags. Each component specifies the type of solution constraint:

\[\begin{split}\texttt{constraints[i]} = \left\{ \begin{array}{rcl} 0.0 &\Rightarrow\;& \text{no constraint is imposed on}\; y_i,\\ 1.0 &\Rightarrow\;& y_i \geq 0,\\ -1.0 &\Rightarrow\;& y_i \leq 0,\\ 2.0 &\Rightarrow\;& y_i > 0,\\ -2.0 &\Rightarrow\;& y_i < 0.\\ \end{array}\right.\end{split}\]

Return value:

ARK_SUCCESS if successful
ARK_MEM_NULL if the ERKStep memory is NULL
ARK_ILL_INPUT if the constraints vector contains illegal values

Notes:

The presence of a non-NULL constraints vector that is not 0.0 in all components will cause constraint checking to be performed. However, a call with 0.0 in all components of constraints will result in an illegal input return. A NULL constraints vector will disable constraint checking.

After a call to ERKStepResize() inequality constraint checking will be disabled and a call to ERKStepSetConstraints() is required to re-enable constraint checking.

Since constraint-handling is performed through cutting time steps that would violate the constraints, it is possible that this feature will cause some problems to fail due to an inability to enforce constraints even at the minimum time step size. Additionally, the features ERKStepSetConstraints() and ERKStepSetFixedStep() are incompatible, and should not be used simultaneously.

Deprecated since version 6.1.0: Use ARKodeSetConstraints() instead.

int ERKStepSetMaxNumConstrFails(void *arkode_mem, int maxfails)

Specifies the maximum number of constraint failures in a step before ERKStep will return with an error.

Arguments:

arkode_mem – pointer to the ERKStep memory block.
maxfails – maximum allowed number of constrain failures.

Return value:

ARK_SUCCESS if successful
ARK_MEM_NULL if the ERKStep memory is NULL

Notes:

Passing maxfails <= 0 results in ERKStep using the default value (10).

Deprecated since version 6.1.0: Use ARKodeSetMaxNumConstrFails() instead.

2.4.8.1.5.2. Optional inputs for IVP method selection

Table 2.3 Optional inputs for IVP method selection
Optional input	Function name	Default
Set integrator method order	`ERKStepSetOrder()`	4
Set explicit RK table	`ERKStepSetTable()`	internal
Set explicit RK table via its number	`ERKStepSetTableNum()`	internal
Set explicit RK table via its name	`ERKStepSetTableName()`	internal

int ERKStepSetOrder(void *arkode_mem, int ord)

Specifies the order of accuracy for the ERK integration method.

Arguments:

arkode_mem – pointer to the ERKStep memory block.
ord – requested order of accuracy.

Return value:

ARK_SUCCESS if successful
ARK_MEM_NULL if the ERKStep memory is NULL
ARK_ILL_INPUT if an argument had an illegal value

Notes:

The allowed values are \(2 \le\) ord \(\le 8\). Any illegal input will result in the default value of 4.

Since ord affects the memory requirements for the internal ERKStep memory block, it cannot be changed after the first call to ERKStepEvolve(), unless ERKStepReInit() is called.

Deprecated since version 6.1.0: Use ARKodeSetOrder() instead.

int ERKStepSetTable(void *arkode_mem, ARKodeButcherTable B)

Specifies a customized Butcher table for the ERK method.

Arguments:

arkode_mem – pointer to the ERKStep memory block.
B – the Butcher table for the explicit RK method.

Return value:

ARK_SUCCESS if successful
ARK_MEM_NULL if the ERKStep memory is NULL
ARK_ILL_INPUT if an argument had an illegal value

Notes:

For a description of the ARKodeButcherTable type and related functions for creating Butcher tables, see §2.5.

No error checking is performed to ensure that either the method order p or the embedding order q specified in the Butcher table structure correctly describe the coefficients in the Butcher table.

Error checking is performed to ensure that the Butcher table is strictly lower-triangular (i.e. that it specifies an ERK method).

If the Butcher table does not contain an embedding, the user must call ERKStepSetFixedStep() to enable fixed-step mode and set the desired time step size.

Warning:: This should not be used with ARKodeSetOrder().

int ERKStepSetTableNum(void *arkode_mem, ARKODE_ERKTableID etable)

Indicates to use a specific built-in Butcher table for the ERK method.

Arguments:

arkode_mem – pointer to the ERKStep memory block.
etable – index of the Butcher table.

Return value:

ARK_SUCCESS if successful
ARK_MEM_NULL if the ERKStep memory is NULL
ARK_ILL_INPUT if an argument had an illegal value

Notes:

etable should match an existing explicit method from §2.8.1. Error-checking is performed to ensure that the table exists, and is not implicit.

Warning:

This should not be used with ARKodeSetOrder().

int ERKStepSetTableName(void *arkode_mem, const char *etable)

Indicates to use a specific built-in Butcher table for the ERK method.

Arguments:

arkode_mem – pointer to the ERKStep memory block.
etable – name of the Butcher table.

Return value:

ARK_SUCCESS if successful
ARK_MEM_NULL if the ERKStep memory is NULL
ARK_ILL_INPUT if an argument had an illegal value

Notes:

etable should match an existing explicit method from §2.8.1. Error-checking is performed to ensure that the table exists, and is not implicit. This function is case sensitive.

Warning:

This should not be used with ARKodeSetOrder().

2.4.8.1.5.3. Optional inputs for time step adaptivity

The mathematical explanation of ARKODE’s time step adaptivity algorithm, including how each of the parameters below is used within the code, is provided in §2.2.11.

int ERKStepSetAdaptController(void *arkode_mem, SUNAdaptController C)

Sets a user-supplied time-step controller object.

Arguments:

arkode_mem – pointer to the ERKStep memory block.
C – user-supplied time adaptivity controller. If NULL then the I controller will be created (see §12.2).

Return value:

ARK_SUCCESS if successful
ARK_MEM_NULL if the ERKStep memory is NULL
ARK_MEM_FAIL if C was NULL and the I controller could not be allocated.

Added in version 5.7.0.

Deprecated since version 6.1.0: Use ARKodeSetAdaptController() instead.

Changed in version 6.3.0: The default controller was changed from PI to I. Additionally, in prior versions, passing NULL to this function would attach the PID controller.

int ERKStepSetAdaptivityFn(void *arkode_mem, ARKAdaptFn hfun, void *h_data)

Sets a user-supplied time-step adaptivity function.

Arguments:

arkode_mem – pointer to the ERKStep memory block.
hfun – name of user-supplied adaptivity function.
h_data – pointer to user data passed to hfun every time it is called.

Return value:

ARK_SUCCESS if successful
ARK_MEM_NULL if the ERKStep memory is NULL
ARK_ILL_INPUT if an argument had an illegal value

Notes:

This function should focus on accuracy-based time step estimation; for stability based time steps the function ERKStepSetStabilityFn() should be used instead.

Deprecated since version 5.7.0: Use the SUNAdaptController infrastructure instead (see §12.1).

int ERKStepSetAdaptivityMethod(void *arkode_mem, int imethod, int idefault, int pq, sunrealtype *adapt_params)

Specifies the method (and associated parameters) used for time step adaptivity.

Arguments:

arkode_mem – pointer to the ERKStep memory block.
imethod – accuracy-based adaptivity method choice (0 \(\le\) imethod \(\le\) 5): 0 is PID, 1 is PI, 2 is I, 3 is explicit Gustafsson, 4 is implicit Gustafsson, and 5 is the ImEx Gustafsson.
idefault – flag denoting whether to use default adaptivity parameters (1), or that they will be supplied in the adapt_params argument (0).
pq – flag denoting whether to use the embedding order of accuracy p (0), the method order of accuracy q (1), or the minimum of the two (any input not equal to 0 or 1) within the adaptivity algorithm. p is the default.
adapt_params[0] – \(k_1\) parameter within accuracy-based adaptivity algorithms.
adapt_params[1] – \(k_2\) parameter within accuracy-based adaptivity algorithms.
adapt_params[2] – \(k_3\) parameter within accuracy-based adaptivity algorithms.

Return value:

ARK_SUCCESS if successful
ARK_MEM_NULL if the ERKStep memory is NULL
ARK_ILL_INPUT if an argument had an illegal value

Notes:

If custom parameters are supplied, they will be checked for validity against published stability intervals. If other parameter values are desired, it is recommended to instead provide a custom function through a call to ERKStepSetAdaptivityFn().

Changed in version 5.7.0: Prior to version 5.7.0, any nonzero value for pq would result in use of the embedding order of accuracy.

Deprecated since version 5.7.0: Use the SUNAdaptController infrastructure instead (see §12.1).

int ERKStepSetAdaptivityAdjustment(void *arkode_mem, int adjust)

Called by a user to adjust the method order supplied to the temporal adaptivity controller. For example, if the user expects order reduction due to problem stiffness, they may request that the controller assume a reduced order of accuracy for the method by specifying a value \(adjust < 0\).

Arguments:

arkode_mem – pointer to the ERKStep memory block.
adjust – adjustment factor (default is 0).

Return value:

ARK_SUCCESS if successful
ARK_MEM_NULL if the ERKStep memory is NULL
ARK_ILL_INPUT if an argument had an illegal value

Notes:

This should be called prior to calling ERKStepEvolve(), and can only be reset following a call to ERKStepReInit().

Added in version 5.7.0.

Deprecated since version 6.1.0: Use ARKodeSetAdaptivityAdjustment() instead.

Changed in version 6.3.0: The default value was changed from -1 to 0

int ERKStepSetCFLFraction(void *arkode_mem, sunrealtype cfl_frac)

Specifies the fraction of the estimated explicitly stable step to use.

Arguments:

arkode_mem – pointer to the ERKStep memory block.
cfl_frac – maximum allowed fraction of explicitly stable step (default is 0.5).

Return value:

ARK_SUCCESS if successful
ARK_MEM_NULL if the ERKStep memory is NULL
ARK_ILL_INPUT if an argument had an illegal value

Notes:

Any non-positive parameter will imply a reset to the default value.

Deprecated since version 6.1.0: Use ARKodeSetCFLFraction() instead.

int ERKStepSetErrorBias(void *arkode_mem, sunrealtype bias)

Specifies the bias to be applied to the error estimates within accuracy-based adaptivity strategies.

Arguments:

arkode_mem – pointer to the ERKStep memory block.
bias – bias applied to error in accuracy-based time step estimation (default is 1.0).

Return value:

ARK_SUCCESS if successful
ARK_MEM_NULL if the ERKStep memory is NULL
ARK_ILL_INPUT if an argument had an illegal value

Notes:

Any value below 1.0 will imply a reset to the default value.

If both this and one of ERKStepSetAdaptivityMethod() or ERKStepSetAdaptController() will be called, then this routine must be called second.

Deprecated since version 5.7.0: Use the SUNAdaptController infrastructure instead (see §12.1).

Changed in version 6.3.0: The default value was changed from 1.5 to 1.0

int ERKStepSetFixedStepBounds(void *arkode_mem, sunrealtype lb, sunrealtype ub)

Specifies the step growth interval in which the step size will remain unchanged.

Arguments:

arkode_mem – pointer to the ERKStep memory block.
lb – lower bound on window to leave step size fixed (default is 1.0).
ub – upper bound on window to leave step size fixed (default is 1.0).

Return value:

ARK_SUCCESS if successful
ARK_MEM_NULL if the ERKStep memory is NULL
ARK_ILL_INPUT if an argument had an illegal value

Notes:

Any interval not containing 1.0 will imply a reset to the default values.

Deprecated since version 6.1.0: Use ARKodeSetFixedStepBounds() instead.

Changed in version 6.3.0: The default upper bound was changed from 1.5 to 1.0

int ERKStepSetMaxEFailGrowth(void *arkode_mem, sunrealtype etamxf)

Specifies the maximum step size growth factor upon multiple successive accuracy-based error failures in the solver.

Arguments:

arkode_mem – pointer to the ERKStep memory block.
etamxf – time step reduction factor on multiple error fails (default is 0.3).

Return value:

ARK_SUCCESS if successful
ARK_MEM_NULL if the ERKStep memory is NULL
ARK_ILL_INPUT if an argument had an illegal value

Notes:

Any value outside the interval \((0,1]\) will imply a reset to the default value.

Deprecated since version 6.1.0: Use ARKodeSetMaxEFailGrowth() instead.

int ERKStepSetMaxFirstGrowth(void *arkode_mem, sunrealtype etamx1)

Specifies the maximum allowed growth factor in step size following the very first integration step.

Arguments:

arkode_mem – pointer to the ERKStep memory block.
etamx1 – maximum allowed growth factor after the first time step (default is 10000.0).

Return value:

ARK_SUCCESS if successful
ARK_MEM_NULL if the ERKStep memory is NULL
ARK_ILL_INPUT if an argument had an illegal value

Notes:

Any value \(\le 1.0\) will imply a reset to the default value.

Deprecated since version 6.1.0: Use ARKodeSetMaxFirstGrowth() instead.

int ERKStepSetMaxGrowth(void *arkode_mem, sunrealtype mx_growth)

Specifies the maximum allowed growth factor in step size between consecutive steps in the integration process.

Arguments:

arkode_mem – pointer to the ERKStep memory block.
mx_growth – maximum allowed growth factor between consecutive time steps (default is 20.0).

Return value:

ARK_SUCCESS if successful
ARK_MEM_NULL if the ERKStep memory is NULL
ARK_ILL_INPUT if an argument had an illegal value

Notes:

Any value \(\le 1.0\) will imply a reset to the default value.

Deprecated since version 6.1.0: Use ARKodeSetMaxGrowth() instead.

int ERKStepSetMinReduction(void *arkode_mem, sunrealtype eta_min)

Specifies the minimum allowed reduction factor in step size between step attempts, resulting from a temporal error failure in the integration process.

Arguments:

arkode_mem – pointer to the ERKStep memory block.
eta_min – minimum allowed reduction factor time step after an error test failure (default is 0.1).

Return value:

ARK_SUCCESS if successful
ARK_MEM_NULL if the ERKStep memory is NULL
ARK_ILL_INPUT if an argument had an illegal value

Notes:

Any value \(\ge 1.0\) or \(\le 0.0\) will imply a reset to the default value.

Deprecated since version 6.1.0: Use ARKodeSetMinReduction() instead.

int ERKStepSetSafetyFactor(void *arkode_mem, sunrealtype safety)

Specifies the safety factor to be applied to the accuracy-based estimated step.

Arguments:

arkode_mem – pointer to the ERKStep memory block.
safety – safety factor applied to accuracy-based time step (default is 0.9).

Return value:

ARK_SUCCESS if successful
ARK_MEM_NULL if the ERKStep memory is NULL
ARK_ILL_INPUT if an argument had an illegal value

Notes:

Any non-positive parameter will imply a reset to the default value.

Deprecated since version 6.1.0: Use ARKodeSetSafetyFactor() instead.

Changed in version 6.3.0: The default default was changed from 0.96 to 0.9. The maximum value is now exactly 1.0 rather than strictly less than 1.0.

int ERKStepSetSmallNumEFails(void *arkode_mem, int small_nef)

Specifies the threshold for “multiple” successive error failures before the etamxf parameter from ERKStepSetMaxEFailGrowth() is applied.

Arguments:

arkode_mem – pointer to the ERKStep memory block.
small_nef – bound to determine “multiple” for etamxf (default is 2).

Return value:

ARK_SUCCESS if successful
ARK_MEM_NULL if the ERKStep memory is NULL
ARK_ILL_INPUT if an argument had an illegal value

Notes:

Any non-positive parameter will imply a reset to the default value.

Deprecated since version 6.1.0: Use ARKodeSetSmallNumEFails() instead.

int ERKStepSetStabilityFn(void *arkode_mem, ARKExpStabFn EStab, void *estab_data)

Sets the problem-dependent function to estimate a stable time step size for the explicit portion of the ODE system.

Arguments:

arkode_mem – pointer to the ERKStep memory block.
EStab – name of user-supplied stability function.
estab_data – pointer to user data passed to EStab every time it is called.

Return value:

ARK_SUCCESS if successful
ARK_MEM_NULL if the ERKStep memory is NULL
ARK_ILL_INPUT if an argument had an illegal value

Notes:

This function should return an estimate of the absolute value of the maximum stable time step for the the ODE system. It is not required, since accuracy-based adaptivity may be sufficient for retaining stability, but this can be quite useful for problems where the right-hand side function \(f(t,y)\) contains stiff terms.

Deprecated since version 6.1.0: Use ARKodeSetStabilityFn() instead.

2.4.8.1.5.4. Rootfinding optional input functions

int ERKStepSetRootDirection(void *arkode_mem, int *rootdir)

Specifies the direction of zero-crossings to be located and returned.

Arguments:

arkode_mem – pointer to the ERKStep memory block.
rootdir – state array of length nrtfn, the number of root functions \(g_i\) (the value of nrtfn was supplied in the call to ERKStepRootInit()). If rootdir[i] == 0 then crossing in either direction for \(g_i\) should be reported. A value of +1 or -1 indicates that the solver should report only zero-crossings where \(g_i\) is increasing or decreasing, respectively.

Return value:

ARK_SUCCESS if successful
ARK_MEM_NULL if the ERKStep memory is NULL
ARK_ILL_INPUT if an argument had an illegal value

Notes:

The default behavior is to monitor for both zero-crossing directions.

Deprecated since version 6.1.0: Use ARKodeSetRootDirection() instead.

int ERKStepSetNoInactiveRootWarn(void *arkode_mem)

Disables issuing a warning if some root function appears to be identically zero at the beginning of the integration.

Arguments:

arkode_mem – pointer to the ERKStep memory block.

Return value:

ARK_SUCCESS if successful
ARK_MEM_NULL if the ERKStep memory is NULL

Notes:

ERKStep will not report the initial conditions as a possible zero-crossing (assuming that one or more components \(g_i\) are zero at the initial time). However, if it appears that some \(g_i\) is identically zero at the initial time (i.e., \(g_i\) is zero at the initial time and after the first step), ERKStep will issue a warning which can be disabled with this optional input function.

Deprecated since version 6.1.0: Use ARKodeSetNoInactiveRootWarn() instead.

2.4.8.1.6. Interpolated output function

int ERKStepGetDky(void *arkode_mem, sunrealtype t, int k, N_Vector dky)

Computes the k-th derivative of the function \(y\) at the time t, i.e., \(y^{(k)}(t)\), for values of the independent variable satisfying \(t_n-h_n \le t \le t_n\), with \(t_n\) as current internal time reached, and \(h_n\) is the last internal step size successfully used by the solver. This routine uses an interpolating polynomial of degree min(degree, 5), where degree is the argument provided to ERKStepSetInterpolantDegree(). The user may request k in the range {0,…, min(degree, kmax)} where kmax depends on the choice of interpolation module. For Hermite interpolants kmax = 5 and for Lagrange interpolants kmax = 3.

Arguments:

arkode_mem – pointer to the ERKStep memory block.
t – the value of the independent variable at which the derivative is to be evaluated.
k – the derivative order requested.
dky – output vector (must be allocated by the user).

Return value:

ARK_SUCCESS if successful
ARK_BAD_K if k is not in the range {0,…, min(degree, kmax)}.
ARK_BAD_T if t is not in the interval \([t_n-h_n, t_n]\)
ARK_BAD_DKY if the dky vector was NULL
ARK_MEM_NULL if the ERKStep memory is NULL

Notes:

It is only legal to call this function after a successful return from ERKStepEvolve().

A user may access the values \(t_n\) and \(h_n\) via the functions ERKStepGetCurrentTime() and ERKStepGetLastStep(), respectively.

Deprecated since version 6.1.0: Use ARKodeGetDky() instead.

2.4.8.1.7. Optional output functions

2.4.8.1.7.1. Main solver optional output functions

int ERKStepGetWorkSpace(void *arkode_mem, long int *lenrw, long int *leniw)

Returns the ERKStep real and integer workspace sizes.

Arguments:

arkode_mem – pointer to the ERKStep memory block.
lenrw – the number of sunrealtype values in the ERKStep workspace.
leniw – the number of integer values in the ERKStep workspace.

Return value:

ARK_SUCCESS if successful
ARK_MEM_NULL if the ERKStep memory was NULL

Deprecated since version 6.1.0: Use ARKodeGetWorkSpace() instead.

int ERKStepGetNumSteps(void *arkode_mem, long int *nsteps)

Returns the cumulative number of internal steps taken by the solver (so far).

Arguments:

arkode_mem – pointer to the ERKStep memory block.
nsteps – number of steps taken in the solver.

Return value:

ARK_SUCCESS if successful
ARK_MEM_NULL if the ERKStep memory was NULL

Deprecated since version 6.1.0: Use ARKodeGetNumSteps() instead.

int ERKStepGetActualInitStep(void *arkode_mem, sunrealtype *hinused)

Returns the value of the integration step size used on the first step.

Arguments:

arkode_mem – pointer to the ERKStep memory block.
hinused – actual value of initial step size.

Return value:

ARK_SUCCESS if successful
ARK_MEM_NULL if the ERKStep memory was NULL

Notes:

Even if the value of the initial integration step was specified by the user through a call to ERKStepSetInitStep(), this value may have been changed by ERKStep to ensure that the step size fell within the prescribed bounds \((h_{min} \le h_0 \le h_{max})\), or to satisfy the local error test condition.

Deprecated since version 6.1.0: Use ARKodeGetActualInitStep() instead.

int ERKStepGetLastStep(void *arkode_mem, sunrealtype *hlast)

Returns the integration step size taken on the last successful internal step.

Arguments:

arkode_mem – pointer to the ERKStep memory block.
hlast – step size taken on the last internal step.

Return value:

ARK_SUCCESS if successful
ARK_MEM_NULL if the ERKStep memory was NULL

Deprecated since version 6.1.0: Use ARKodeGetLastStep() instead.

int ERKStepGetCurrentStep(void *arkode_mem, sunrealtype *hcur)

Returns the integration step size to be attempted on the next internal step.

Arguments:

arkode_mem – pointer to the ERKStep memory block.
hcur – step size to be attempted on the next internal step.

Return value:

ARK_SUCCESS if successful
ARK_MEM_NULL if the ERKStep memory was NULL

Deprecated since version 6.1.0: Use ARKodeGetCurrentStep() instead.

int ERKStepGetCurrentTime(void *arkode_mem, sunrealtype *tcur)

Returns the current internal time reached by the solver.

Arguments:

arkode_mem – pointer to the ERKStep memory block.
tcur – current internal time reached.

Return value:

ARK_SUCCESS if successful
ARK_MEM_NULL if the ERKStep memory was NULL

Deprecated since version 6.1.0: Use ARKodeGetCurrentTime() instead.

int ERKStepGetTolScaleFactor(void *arkode_mem, sunrealtype *tolsfac)

Returns a suggested factor by which the user’s tolerances should be scaled when too much accuracy has been requested for some internal step.

Arguments:

arkode_mem – pointer to the ERKStep memory block.
tolsfac – suggested scaling factor for user-supplied tolerances.

Return value:

ARK_SUCCESS if successful
ARK_MEM_NULL if the ERKStep memory was NULL

Deprecated since version 6.1.0: Use ARKodeGetTolScaleFactor() instead.

int ERKStepGetErrWeights(void *arkode_mem, N_Vector eweight)

Returns the current error weight vector.

Arguments:

arkode_mem – pointer to the ERKStep memory block.
eweight – solution error weights at the current time.

Return value:

ARK_SUCCESS if successful
ARK_MEM_NULL if the ERKStep memory was NULL

Notes:

The user must allocate space for eweight, that will be filled in by this function.

Deprecated since version 6.1.0: Use ARKodeGetErrWeights() instead.

int ERKStepGetStepStats(void *arkode_mem, long int *nsteps, sunrealtype *hinused, sunrealtype *hlast, sunrealtype *hcur, sunrealtype *tcur)

Returns many of the most useful optional outputs in a single call.

Arguments:

arkode_mem – pointer to the ERKStep memory block.
nsteps – number of steps taken in the solver.
hinused – actual value of initial step size.
hlast – step size taken on the last internal step.
hcur – step size to be attempted on the next internal step.
tcur – current internal time reached.

Return value:

ARK_SUCCESS if successful
ARK_MEM_NULL if the ERKStep memory was NULL

Deprecated since version 6.1.0: Use ARKodeGetStepStats() instead.

int ERKStepPrintAllStats(void *arkode_mem, FILE *outfile, SUNOutputFormat fmt)

Outputs all of the integrator and other statistics.

Arguments:

arkode_mem – pointer to the ERKStep memory block.
outfile – pointer to output file.
fmt – the output format:
- SUN_OUTPUTFORMAT_TABLE – prints a table of values
- SUN_OUTPUTFORMAT_CSV – prints a comma-separated list of key and value pairs e.g., key1,value1,key2,value2,...

Return value:

ARK_SUCCESS – if the output was successfully.
CV_MEM_NULL – if the ERKStep memory was NULL.
CV_ILL_INPUT – if an invalid formatting option was provided.

Note

The Python module tools/suntools provides utilities to read and output the data from a SUNDIALS CSV output file using the key and value pair format.

Added in version 5.2.0.

Deprecated since version 6.1.0: Use ARKodePrintAllStats() instead.

char *ERKStepGetReturnFlagName(long int flag)

Returns the name of the ERKStep constant corresponding to flag. See ARKODE Constants.

Arguments:

flag – a return flag from an ERKStep function.

Return value:

The return value is a string containing the name of the corresponding constant.

Deprecated since version 6.1.0: Use ARKodeGetReturnFlagName() instead.

int ERKStepGetNumExpSteps(void *arkode_mem, long int *expsteps)

Returns the cumulative number of stability-limited steps taken by the solver (so far).

Arguments:

arkode_mem – pointer to the ERKStep memory block.
expsteps – number of stability-limited steps taken in the solver.

Return value:

ARK_SUCCESS if successful
ARK_MEM_NULL if the ERKStep memory was NULL

Deprecated since version 6.1.0: Use ARKodeGetNumExpSteps() instead.

int ERKStepGetNumAccSteps(void *arkode_mem, long int *accsteps)

Returns the cumulative number of accuracy-limited steps taken by the solver (so far).

Arguments:

arkode_mem – pointer to the ERKStep memory block.
accsteps – number of accuracy-limited steps taken in the solver.

Return value:

ARK_SUCCESS if successful
ARK_MEM_NULL if the ERKStep memory was NULL

Deprecated since version 6.1.0: Use ARKodeGetNumAccSteps() instead.

int ERKStepGetNumStepAttempts(void *arkode_mem, long int *step_attempts)

Returns the cumulative number of steps attempted by the solver (so far).

Arguments:

arkode_mem – pointer to the ERKStep memory block.
step_attempts – number of steps attempted by solver.

Return value:

ARK_SUCCESS if successful
ARK_MEM_NULL if the ERKStep memory was NULL

Deprecated since version 6.1.0: Use ARKodeGetNumStepAttempts() instead.

int ERKStepGetNumRhsEvals(void *arkode_mem, long int *nf_evals)

Returns the number of calls to the user’s right-hand side function, \(f\) (so far).

Arguments:

arkode_mem – pointer to the ERKStep memory block.
nf_evals – number of calls to the user’s \(f(t,y)\) function.

Return value:

ARK_SUCCESS if successful
ARK_MEM_NULL if the ERKStep memory was NULL

Deprecated since version 6.2.0: Use ARKodeGetNumRhsEvals() instead.

int ERKStepGetNumErrTestFails(void *arkode_mem, long int *netfails)

Returns the number of local error test failures that have occurred (so far).

Arguments:

arkode_mem – pointer to the ERKStep memory block.
netfails – number of error test failures.

Return value:

ARK_SUCCESS if successful
ARK_MEM_NULL if the ERKStep memory was NULL

Deprecated since version 6.1.0: Use ARKodeGetNumErrTestFails() instead.

int ERKStepGetCurrentButcherTable(void *arkode_mem, ARKodeButcherTable *B)

Returns the Butcher table currently in use by the solver.

Arguments:

arkode_mem – pointer to the ERKStep memory block.
B – pointer to the Butcher table structure.

Return value:

ARK_SUCCESS if successful
ARK_MEM_NULL if the ERKStep memory was NULL

Notes:

The ARKodeButcherTable data structure is defined as a pointer to the following C structure:

typedef struct ARKodeButcherTableMem {

  int q;              /* method order of accuracy       */
  int p;              /* embedding order of accuracy    */
  int stages;         /* number of stages               */
  sunrealtype **A;    /* Butcher table coefficients     */
  sunrealtype *c;     /* canopy node coefficients       */
  sunrealtype *b;     /* root node coefficients         */
  sunrealtype *d;     /* embedding coefficients         */

} *ARKodeButcherTable;

For more details see §2.5.

int ERKStepGetEstLocalErrors(void *arkode_mem, N_Vector ele)

Returns the vector of estimated local truncation errors for the current step.

Arguments:

arkode_mem – pointer to the ERKStep memory block.
ele – vector of estimated local truncation errors.

Return value:

ARK_SUCCESS if successful
ARK_MEM_NULL if the ERKStep memory was NULL

Notes:

The user must allocate space for ele, that will be filled in by this function.

The values returned in ele are valid only after a successful call to ERKStepEvolve() (i.e., it returned a non-negative value).

The ele vector, together with the eweight vector from ERKStepGetErrWeights(), can be used to determine how the various components of the system contributed to the estimated local error test. Specifically, that error test uses the WRMS norm of a vector whose components are the products of the components of these two vectors. Thus, for example, if there were recent error test failures, the components causing the failures are those with largest values for the products, denoted loosely as eweight[i]*ele[i].

Deprecated since version 6.1.0: Use ARKodeGetEstLocalErrors() instead.

int ERKStepGetTimestepperStats(void *arkode_mem, long int *expsteps, long int *accsteps, long int *step_attempts, long int *nf_evals, long int *netfails)

Returns many of the most useful time-stepper statistics in a single call.

Arguments:

arkode_mem – pointer to the ERKStep memory block.
expsteps – number of stability-limited steps taken in the solver.
accsteps – number of accuracy-limited steps taken in the solver.
step_attempts – number of steps attempted by the solver.
nf_evals – number of calls to the user’s \(f(t,y)\) function.
netfails – number of error test failures.

Return value:

ARK_SUCCESS if successful
ARK_MEM_NULL if the ERKStep memory was NULL

int ERKStepGetNumConstrFails(void *arkode_mem, long int *nconstrfails)

Returns the cumulative number of constraint test failures (so far).

Arguments:

arkode_mem – pointer to the ERKStep memory block.
nconstrfails – number of constraint test failures.

Return value:

ARK_SUCCESS if successful
ARK_MEM_NULL if the ERKStep memory was NULL

Deprecated since version 6.1.0: Use ARKodeGetNumConstrFails() instead.

int ERKStepGetUserData(void *arkode_mem, void **user_data)

Returns the user data pointer previously set with ERKStepSetUserData().

Arguments:

arkode_mem – pointer to the ERKStep memory block.
user_data – memory reference to a user data pointer

Return value:

ARK_SUCCESS if successful
ARK_MEM_NULL if the ERKStep memory was NULL

Added in version 5.3.0.

Deprecated since version 6.1.0: Use ARKodeGetUserData() instead.

2.4.8.1.7.2. Rootfinding optional output functions

int ERKStepGetRootInfo(void *arkode_mem, int *rootsfound)

Returns an array showing which functions were found to have a root.

Arguments:

arkode_mem – pointer to the ERKStep memory block.
rootsfound – array of length nrtfn with the indices of the user functions \(g_i\) found to have a root (the value of nrtfn was supplied in the call to ERKStepRootInit()). For \(i = 0 \ldots\) nrtfn-1, rootsfound[i] is nonzero if \(g_i\) has a root, and 0 if not.

Return value:

ARK_SUCCESS if successful
ARK_MEM_NULL if the ERKStep memory was NULL

Notes:

The user must allocate space for rootsfound prior to calling this function.

For the components of \(g_i\) for which a root was found, the sign of rootsfound[i] indicates the direction of zero-crossing. A value of +1 indicates that \(g_i\) is increasing, while a value of -1 indicates a decreasing \(g_i\).

Deprecated since version 6.1.0: Use ARKodeGetRootInfo() instead.

int ERKStepGetNumGEvals(void *arkode_mem, long int *ngevals)

Returns the cumulative number of calls made to the user’s root function \(g\).

Arguments:

arkode_mem – pointer to the ERKStep memory block.
ngevals – number of calls made to \(g\) so far.

Return value:

ARK_SUCCESS if successful
ARK_MEM_NULL if the ERKStep memory was NULL

Deprecated since version 6.1.0: Use ARKodeGetNumGEvals() instead.

2.4.8.1.7.3. General usability functions

int ERKStepWriteParameters(void *arkode_mem, FILE *fp)

Outputs all ERKStep solver parameters to the provided file pointer.

Arguments:

arkode_mem – pointer to the ERKStep memory block.
fp – pointer to use for printing the solver parameters.

Return value:

ARK_SUCCESS if successful
ARK_MEM_NULL if the ERKStep memory was NULL

Notes:

The fp argument can be stdout or stderr, or it may point to a specific file created using fopen.

When run in parallel, only one process should set a non-NULL value for this pointer, since parameters for all processes would be identical.

Deprecated since version 6.1.0: Use ARKodeWriteParameters() instead.

int ERKStepWriteButcher(void *arkode_mem, FILE *fp)

Outputs the current Butcher table to the provided file pointer.

Arguments:

arkode_mem – pointer to the ERKStep memory block.
fp – pointer to use for printing the Butcher table.

Return value:

ARK_SUCCESS if successful
ARK_MEM_NULL if the ERKStep memory was NULL

Notes:

The fp argument can be stdout or stderr, or it may point to a specific file created using fopen.

When run in parallel, only one process should set a non-NULL value for this pointer, since tables for all processes would be identical.

Deprecated since version 6.1.0: Use ERKStepGetCurrentButcherTable() and ARKodeButcherTable_Write() instead.

2.4.8.1.8. ERKStep re-initialization function

To reinitialize the ERKStep module for the solution of a new problem, where a prior call to ERKStepCreate() has been made, the user must call the function ERKStepReInit(). The new problem must have the same size as the previous one. This routine retains the current settings for all ERKstep module options and performs the same input checking and initializations that are done in ERKStepCreate(), but it performs no memory allocation as it assumes that the existing internal memory is sufficient for the new problem. A call to this re-initialization routine deletes the solution history that was stored internally during the previous integration, and deletes any previously-set tstop value specified via a call to ERKStepSetStopTime(). Following a successful call to ERKStepReInit(), call ERKStepEvolve() again for the solution of the new problem.

The use of ERKStepReInit() requires that the number of Runge–Kutta stages, denoted by s, be no larger for the new problem than for the previous problem. This condition is automatically fulfilled if the method order q is left unchanged.

One important use of the ERKStepReInit() function is in the treating of jump discontinuities in the RHS function. Except in cases of fairly small jumps, it is usually more efficient to stop at each point of discontinuity and restart the integrator with a readjusted ODE model, using a call to this routine. To stop when the location of the discontinuity is known, simply make that location a value of tout. To stop when the location of the discontinuity is determined by the solution, use the rootfinding feature. In either case, it is critical that the RHS function not incorporate the discontinuity, but rather have a smooth extension over the discontinuity, so that the step across it (and subsequent rootfinding, if used) can be done efficiently. Then use a switch within the RHS function (communicated through user_data) that can be flipped between the stopping of the integration and the restart, so that the restarted problem uses the new values (which have jumped). Similar comments apply if there is to be a jump in the dependent variable vector.

int ERKStepReInit(void *arkode_mem, ARKRhsFn f, sunrealtype t0, N_Vector y0)

Provides required problem specifications and re-initializes the ERKStep time-stepper module.

Arguments:

arkode_mem – pointer to the ERKStep memory block.
f – the name of the C function (of type ARKRhsFn()) defining the right-hand side function in \(\dot{y} = f(t,y)\).
t0 – the initial value of \(t\).
y0 – the initial condition vector \(y(t_0)\).

Return value:

ARK_SUCCESS if successful
ARK_MEM_NULL if the ERKStep memory was NULL
ARK_MEM_FAIL if a memory allocation failed
ARK_ILL_INPUT if an argument had an illegal value.

Notes:

All previously set options are retained but may be updated by calling the appropriate “Set” functions.

If an error occurred, ERKStepReInit() also sends an error message to the error handler function.

2.4.8.1.9. ERKStep reset function

int ERKStepReset(void *arkode_mem, sunrealtype tR, N_Vector yR)

Resets the current ERKStep time-stepper module state to the provided independent variable value and dependent variable vector.

Arguments:

arkode_mem – pointer to the ERKStep memory block.
tR – the value of the independent variable \(t\).
yR – the value of the dependent variable vector \(y(t_R)\).

Return value:

ARK_SUCCESS if successful
ARK_MEM_NULL if the ERKStep memory was NULL
ARK_MEM_FAIL if a memory allocation failed
ARK_ILL_INPUT if an argument had an illegal value.

Notes:

By default the next call to ERKStepEvolve() will use the step size computed by ERKStep prior to calling ERKStepReset(). To set a different step size or have ERKStep estimate a new step size use ERKStepSetInitStep().

All previously set options are retained but may be updated by calling the appropriate “Set” functions.

If an error occurred, ERKStepReset() also sends an error message to the error handler function.

Deprecated since version 6.1.0: Use ARKodeReset() instead.

2.4.8.1.10. ERKStep system resize function

int ERKStepResize(void *arkode_mem, N_Vector yR, sunrealtype hscale, sunrealtype tR, ARKVecResizeFn resize, void *resize_data)

Re-sizes ERKStep with a different state vector but with comparable dynamical time scale.

Arguments:

arkode_mem – pointer to the ERKStep memory block.
yR – the newly-sized solution vector, holding the current dependent variable values \(y(t_R)\).
hscale – the desired time step scaling factor (i.e. the next step will be of size h*hscale).
tR – the current value of the independent variable \(t_R\) (this must be consistent with yR).
resize – the user-supplied vector resize function (of type ARKVecResizeFn().
resize_data – the user-supplied data structure to be passed to resize when modifying internal ERKStep vectors.

Return value:

ARK_SUCCESS if successful
ARK_MEM_NULL if the ERKStep memory was NULL
ARK_NO_MALLOC if arkode_mem was not allocated.
ARK_ILL_INPUT if an argument had an illegal value.

Notes:

If an error occurred, ERKStepResize() also sends an error message to the error handler function.

If inequality constraint checking is enabled a call to ERKStepResize() will disable constraint checking. A call to ERKStepSetConstraints() is required to re-enable constraint checking.

Deprecated since version 6.1.0: Use ARKodeResize() instead.