L-stable embedded Rosenbrock ODE solver of order (3)4. More...
Public Member Functions | |
TypeName ("Rosenbrock34") | |
Runtime type information. More... | |
Rosenbrock34 (const ODESystem &ode, const dictionary &dict) | |
Construct from ODE. More... | |
scalar | solve (const scalar x0, const scalarField &y0, const scalarField &dydx0, const scalar dx, scalarField &y) const |
Solve a single step dx and return the error. More... | |
void | solve (scalar &x, scalarField &y, scalar &dxTry) const |
Solve the ODE system and the update the state. More... | |
Public Member Functions inherited from ODESolver | |
TypeName ("ODESolver") | |
Runtime type information. More... | |
declareRunTimeSelectionTable (autoPtr, ODESolver, dictionary,(const ODESystem &ode, const dictionary &dict),(ode, dict)) | |
ODESolver (const ODESystem &ode, const dictionary &dict) | |
Construct for given ODESystem. More... | |
ODESolver (const ODESystem &ode, const scalarField &absTol, const scalarField &relTol) | |
Construct for given ODESystem specifying tolerances. More... | |
virtual | ~ODESolver () |
Destructor. More... | |
scalarField & | absTol () |
scalarField & | relTol () |
virtual void | solve (scalar &x, scalarField &y, stepState &step) const |
Solve the ODE system as far as possible upto dxTry. More... | |
virtual void | solve (const scalar xStart, const scalar xEnd, scalarField &y, scalar &dxEst) const |
Solve the ODE system from xStart to xEnd, update the state. More... | |
Public Member Functions inherited from adaptiveSolver | |
adaptiveSolver (const ODESystem &ode, const dictionary &dict) | |
Construct from ODESystem. More... | |
virtual | ~adaptiveSolver () |
Destructor. More... | |
void | solve (const ODESystem &ode, scalar &x, scalarField &y, scalar &dxTry) const |
Solve the ODE system and the update the state. More... | |
Additional Inherited Members | |
Static Public Member Functions inherited from ODESolver | |
static autoPtr< ODESolver > | New (const ODESystem &ode, const dictionary &dict) |
Select null constructed. More... | |
Protected Member Functions inherited from ODESolver | |
scalar | normalizeError (const scalarField &y0, const scalarField &y, const scalarField &err) const |
Return the nomalized scalar error. More... | |
ODESolver (const ODESolver &) | |
Disallow default bitwise copy construct. More... | |
void | operator= (const ODESolver &) |
Disallow default bitwise assignment. More... | |
Protected Attributes inherited from ODESolver | |
const ODESystem & | odes_ |
Reference to ODESystem. More... | |
label | n_ |
Size of the ODESystem. More... | |
scalarField | absTol_ |
Absolute convergence tolerance per step. More... | |
scalarField | relTol_ |
Relative convergence tolerance per step. More... | |
label | maxSteps_ |
The maximum number of sub-steps allowed for the integration step. More... | |
L-stable embedded Rosenbrock ODE solver of order (3)4.
"Solving Ordinary Differential Equations II: Stiff and Differential-Algebraic Problems, second edition", Hairer, E., Nørsett, S., Wanner, G., Springer-Verlag, Berlin. 1996.
The default constants are from:
"Implementation of Rosenbrock Methods" Shampine, L. F., ACM Transactions on Mathematical Software, vol. 8, 1982, pp. 93–113.
with which the scheme is more accurate than with the L-Stable coefficients for small step-size but less stable for large step-size.
The L-Stable scheme constants are provided commented-out in Rosenbrock34.C
Definition at line 69 of file Rosenbrock34.H.
Rosenbrock34 | ( | const ODESystem & | ode, |
const dictionary & | dict | ||
) |
Construct from ODE.
Definition at line 108 of file Rosenbrock34.C.
References Rosenbrock34::solve().
TypeName | ( | "Rosenbrock34" | ) |
Runtime type information.
|
virtual |
Solve a single step dx and return the error.
Implements adaptiveSolver.
Definition at line 128 of file Rosenbrock34.C.
References ODESystem::derivatives(), forAll, ODESystem::jacobian(), Foam::LUBacksubstitute(), Foam::LUDecompose(), ODESolver::n_, ODESolver::normalizeError(), and ODESolver::odes_.
Referenced by Rosenbrock34::Rosenbrock34().
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virtual |
Solve the ODE system and the update the state.
Reimplemented from ODESolver.
Definition at line 209 of file Rosenbrock34.C.
References ODESolver::odes_, and adaptiveSolver::solve().