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().
|
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().
1.8.11