User Documentation for SUNDIALS
USAGE
1. Getting Started
2. ARKODE Documentation
3. CVODE Documentation
4. CVODES Documentation
5. IDA Documentation
6. IDAS Documentation
7. KINSOL Documentation
8. Vector Data Structures
9. Matrix Data Structures
10. Linear Algebraic Solvers
11. Nonlinear Algebraic Solvers
12. Time Step Adaptivity Controllers
13. Stepper Data Structure
14. Adjoint Sensitivity Analysis
15. Tools for Memory Management
16. Release History
17. Changelog
18. Frequently Asked Questions
DEVELOPMENT
Contributing
Developer Guide
History
Getting Started
Source Code
Documentation
Testing
Benchmarks
Pull Requests
Releases
Packages
ARKODE
ERKStep Full RHS
ARKStep Full RHS
CVODE
Appendix
REFERENCES
Bibliography
Index
User Documentation for SUNDIALS
Developer Guide
Packages
ARKODE
ERKStep Full RHS
ERKStep Full RHS
ARKStep Full RHS
Fig. 1
ARKStep Full RHS Start
Fig. 2
ARKStep Full RHS End
![digraph erk_fullrhs {
node [shape=box]
splines=ortho
// -----------------
// Before first step
// -----------------
init [label="Initialize integrator\lCopy t0, y0 to tn, yn\l"]
f0cur [label="Set fn_is_current to False", style=filled, fillcolor=tomato1]
h0 [label="Is h0 provided?", target="_top"]
f0_q1 [label="Has f(tn, yn) been computed?"]
eval1 [label="Evaluate f(tn, yn)\lStore in F[0]\lCopy F[0] to fn\l", style=filled, fillcolor=lightskyblue]
fcur1 [label="Set fn_is_current to True", style=filled, fillcolor=lightgreen]
h0_comp [label="Compute h0"]
start [label="Start Step"]
init -> f0cur -> h0
h0 -> start [taillabel="Yes", labeldistance=2, labelangle=45]
h0 -> f0_q1 [taillabel="No", labeldistance=2, labelangle=-45]
f0_q1 -> h0_comp [taillabel="Yes", labeldistance=2, labelangle=-45]
f0_q1 -> eval1 [taillabel="No", labeldistance=2, labelangle=-45]
eval1 -> fcur1
fcur1 -> h0_comp
h0_comp -> start
// ----------
// First step
// ----------
f0q2 [label="Has f(tn, yn) been computed?"]
step_q [label="Is this the first step after initial setup?"]
eval2 [label="Evaluate f(tn, yn)\lStore in F[0]\lCopy F[0] to fn\l", style=filled, fillcolor=lightskyblue]
fsal [label="Is the method FSAL?", style=filled, fillcolor=slateblue1]
eval3 [label="Evaluate f(tn, yn)\lStore in F[0]\lCopy F[0] to fn\l", style=filled, fillcolor=slateblue1]
copy1 [label="Copy F[s-1] to F[0]\lCopy F[0] to fn\l", style=filled, fillcolor=slateblue1]
fcur2 [label="Set fn_is_current to True", style=filled, fillcolor=lightgreen]
stages1 [label="Compute Stages"]
complete [label="Complete Step"]
start -> f0q2
f0q2 -> stages1 [taillabel="Yes", labeldistance=2, labelangle=45]
f0q2 -> step_q [taillabel="No", labeldistance=2, labelangle=-45]
step_q -> eval2 [taillabel="Yes", labeldistance=2, labelangle=45]
eval2 -> fcur2
step_q -> fsal [taillabel="No", labeldistance=2, labelangle=-45]
fsal -> eval3 [taillabel="No", labeldistance=2, labelangle=-45]
eval3 -> fcur2
fsal -> copy1 [taillabel="Yes", labeldistance=2, labelangle=45]
copy1 -> fcur2
fcur2 -> stages1 -> complete
// -------------
// Complete step
// -------------
interp_update [label="Interpolation enabled?"]
interp_type1 [label="Using Hermite interpolation?"]
f0q3 [label="Has f(tn, yn) been computed?"]
update_yn [label="Copy tcur, ycur to tn, yn"]
fcur3 [label="Set fn_is_current to False", style=filled, fillcolor=tomato1]
complete -> interp_update
interp_update -> update_yn [taillabel="No", labeldistance=2, labelangle=45]
interp_update -> interp_type1 [taillabel="Yes", labeldistance=2, labelangle=-45]
interp_type1 -> update_yn [taillabel="No", labeldistance=2, labelangle=45]
interp_type1 -> f0q3 [taillabel="Yes", labeldistance=2, labelangle=-45]
f0q3 -> update_yn [taillabel="Yes", labeldistance=2, labelangle=45]
update_yn -> fcur3
// ----------
// After step
// ----------
interp_eval [label="Evaluate interpolant?"]
interp_type2 [label="Using Hermite interpolation?"]
f1q1 [label="Has f(tn, yn) been computed?"]
fsal1 [label="Is the method FSAL?", style=filled, fillcolor=slateblue1]
eval4 [label="Evaluate f(tn, yn)\lStore in F[0]\lCopy F[0] to fn\l", style=filled, fillcolor=slateblue1]
copy2 [label="Copy F[s-1] to F[0]\lCopy F[0] to fn\l", style=filled, fillcolor=slateblue1]
fcur4 [label="Set fn_is_current to True", style=filled, fillcolor=lightgreen]
interp_yout [label="Compute yout"]
step2 [label="Start Next Step"]
fcur3 -> interp_eval
interp_eval -> step2 [taillabel="No", labeldistance=2, labelangle=45]
interp_eval -> interp_type2 [taillabel="Yes", labeldistance=2, labelangle=-45]
interp_type2 -> interp_yout [taillabel="No", labeldistance=2, labelangle=45]
interp_type2 -> f1q1 [taillabel="Yes", labeldistance=2, labelangle=-45]
f1q1 -> fsal1 [taillabel="No", labeldistance=2, labelangle=45]
fsal1 -> eval4 [taillabel="No", labeldistance=2, labelangle=-45]
eval4 -> fcur4
fsal1 -> copy2 [taillabel="Yes", labeldistance=2, labelangle=45]
copy2 -> fcur4
fcur4 -> interp_yout -> step2
}](../../../_images/graphviz-dad94e1bf5c51d1cdd12b769e25da6942847055f.png)
![digraph ark_fullrhs_start {
node [shape=box, style=filled, fillcolor=white]
splines=ortho
bgcolor=lightskyblue
// --------------
// Full RHS Start
// --------------
fcur [label="Has f(tn, yn) been computed?"]
eval [label="Evaluate fe(tn, yn), fi(tn,yn)\lStore in Fe[0], Fi[0]\l"]
mass_a [label="Is there a mass matrix?"]
mass_b [label="Is M time dependent?"]
mass_c [label="Solve M(t) u = Fe[0], M(t) v = Fi[0]\lStore u, v in Fe[0], Fi[0]\lCopy Fe[0] + Fi[0] to f\l"]
mass_d [label="Copy Fe[0] + Fi[0] to f\lSolve M x = f\lCopy x to f\l"]
copy [label="Copy Fe[0] + Fi[0] to f"]
return [label="Set fn_is_current to True", style=filled, fillcolor=lightgreen]
fcur -> copy [taillabel="Yes", labeldistance=2, labelangle=45]
fcur -> eval [taillabel="No", labeldistance=2, labelangle=45]
eval -> mass_a
mass_a -> copy [taillabel="No", labeldistance=2, labelangle=45]
copy -> return
mass_a -> mass_b [taillabel="Yes", labeldistance=2, labelangle=-45]
mass_b -> mass_c [taillabel="Yes", labeldistance=2, labelangle=-45]
mass_c -> return
mass_b -> mass_d [taillabel="No", labeldistance=2, labelangle=45]
mass_d -> return
}](../../../_images/graphviz-6d84c27efc76b62a9dab671365f53df28ba90147.png)
![digraph ark_fullrhs_start {
node [shape=box, style=filled, fillcolor=white]
splines=ortho
bgcolor=slateblue1
// ------------
// Full RHS End
// ------------
fcur [label="Has f(tn, yn) been computed?"]
sa [label="Is the method stiffly accurate?"]
eval [label="Evaluate fe(tn, yn), fi(tn, yn)\lStore in Fe[0], Fi[0]\l"]
mass_a1 [label="Is there a mass matrix?"]
mass_a2 [label="Is there a mass matrix?"]
mass_b1 [label="Is M time dependent?"]
mass_b2 [label="Is M time dependent?"]
mass_c [label="Solve M(t) u = Fe[0], M(t) v = Fi[0]\lStore u, v in Fe[0], Fi[0]\lCopy Fe[0] + Fi[0] to fn\l"]
mass_d1 [label="Solve M x = fn\lCopy x to fn\l"]
mass_d2 [label="Copy Fe[0] + Fi[0] to fn\lSolve M x = fn\lCopy x to fn\l"]
copy_1 [label="Copy Fe[0] + Fi[0] to fn"]
copy_2 [label="Copy Fe[s-1], Fi[s-1] to Fe[0], Fi[0]\lCopy Fe[0] + Fi[0] to fn\l"]
return [label="Set fn_is_current to True", style=filled, fillcolor=lightgreen]
fcur -> copy_1 [taillabel="Yes", labeldistance=2, labelangle=45]
fcur -> sa [taillabel="No", labeldistance=2, labelangle=45]
sa -> copy_2 [taillabel="Yes", labeldistance=2, labelangle=45]
copy_2 -> mass_a1
mass_a1 -> return [taillabel="No", labeldistance=2, labelangle=-45]
mass_a1 -> mass_b1 [taillabel="Yes", labeldistance=2, labelangle=45]
mass_b1 -> mass_d1 [taillabel="No", labeldistance=2, labelangle=-45]
mass_d1 -> return
mass_b1 -> return [taillabel="Yes", labeldistance=2, labelangle=45]
sa -> eval [taillabel="No", labeldistance=2, labelangle=-45]
eval -> mass_a2
mass_a2 -> copy_1 [taillabel="No", labeldistance=2, labelangle=45]
copy_1 -> return
mass_a2 -> mass_b2 [taillabel="Yes", labeldistance=2, labelangle=-45]
mass_b2 -> mass_c [taillabel="Yes", labeldistance=2, labelangle=-45]
mass_c -> return
mass_b2 -> mass_d2 [taillabel="No", labeldistance=2, labelangle=45]
mass_d2 -> return
}](../../../_images/graphviz-4f2ccccb934dfb1b0f964bb15de69436fcf4bdd9.png)
![digraph ark_fullrhs {
node [shape=box]
splines=ortho
// -----------------
// Before first step
// -----------------
init [label="Initialize integrator\lCopy t0, y0 to tn, yn\l"]
f0cur [label="Set fn_is_current to False", style=filled, fillcolor=tomato1]
h0 [label="Is h0 provided?"]
f0_q [label="Has f(tn, yn) been computed?"]
rhs_1 [label="Call Full RHS Start", style=filled, fillcolor=lightskyblue]
h0_comp [label="Compute h0"]
start [label="Start Step"]
init -> f0cur -> h0
h0 -> start [taillabel="Yes", labeldistance=2, labelangle=45]
h0 -> f0_q [taillabel="No", labeldistance=2, labelangle=-45]
f0_q -> h0_comp [taillabel="Yes", labeldistance=2, labelangle=45]
f0_q -> rhs_1 [taillabel="No", labeldistance=2, labelangle=-45]
rhs_1 -> h0_comp
h0_comp -> start
// ----------
// Start step
// ----------
method_q [label="Is the first stage explicit?\nor\nIs the method stiffly accurate and Hermite interpolation is used?"]
step_q [label="Is this the first step after initial setup?"]
fn_q [label="Has f(tn, yn) been computed?"]
rhs_2 [label="Call Full RHS Start", style=filled, fillcolor=lightskyblue]
rhs_3 [label="Call Full RHS End", style=filled, fillcolor=slateblue1]
stages [label="Compute Stages"]
complete [label="Complete Step"]
start -> method_q
method_q -> stages [taillabel="No", labeldistance=2, labelangle=45]
method_q -> fn_q [taillabel="Yes", labeldistance=2, labelangle=-45]
fn_q -> stages [taillabel="Yes", labeldistance=2, labelangle=-45]
fn_q -> step_q [taillabel="No", labeldistance=2, labelangle=-45]
step_q -> rhs_2 [taillabel="Yes", labeldistance=2, labelangle=-45]
step_q -> rhs_3 [taillabel="No", labeldistance=2, labelangle=-45]
rhs_2 -> stages
rhs_3 -> stages
stages -> complete
// -------------
// Complete step
// -------------
interp_update [label="Interpolation enabled?"]
interp_type1 [label="Using Hermite interpolation?"]
f0q3 [label="Has f(tn, yn) been computed?"]
rhs3 [label="Call Full RHS Start", style=filled, fillcolor=lightskyblue]
update_yn [label="Copy tcur, ycur to tn, yn"]
fcur1 [label="Set fn_is_current to False", style=filled, fillcolor=tomato1]
complete -> interp_update
interp_update -> update_yn [taillabel="No", labeldistance=2, labelangle=45]
interp_update -> interp_type1 [taillabel="Yes", labeldistance=2, labelangle=-45]
interp_type1 -> update_yn [taillabel="No", labeldistance=2, labelangle=45]
interp_type1 -> f0q3 [taillabel="Yes", labeldistance=2, labelangle=-45]
f0q3 -> update_yn [taillabel="Yes", labeldistance=2, labelangle=45]
f0q3 -> rhs3 [taillabel="No", labeldistance=2, labelangle=-45]
rhs3 -> update_yn -> fcur1
// ----------
// After step
// ----------
interp_eval [label="Evaluate interpolant?"]
interp_type2 [label="Using Hermite interpolation?"]
f1q1 [label="Has f(tn, yn) been computed?"]
rhs4 [label="Call Full RHS End", style=filled, fillcolor=slateblue1]
interp_yout [label="Compute yout"]
return [label="Start Next Step"]
fcur1 -> interp_eval
interp_eval -> return [taillabel="No", labeldistance=2, labelangle=45]
interp_eval -> interp_type2 [taillabel="Yes", labeldistance=2, labelangle=-45]
interp_type2 -> interp_yout [taillabel="No", labeldistance=2, labelangle=45]
interp_type2 -> f1q1 [taillabel="Yes", labeldistance=2, labelangle=-45]
f1q1 -> interp_yout [taillabel="Yes", labeldistance=2, labelangle=45]
f1q1 -> rhs4 [taillabel="No", labeldistance=2, labelangle=45]
rhs4 -> interp_yout -> return
}](../../../_images/graphviz-47d3e4ffaa14778d2c2bb66e190e66997d29e994.png)