4/5th Order Runge-Kutta-Fehlberg ODE solver More...
Public Member Functions | |
TypeName ("RKF45") | |
Runtime type information. More... | |
RKF45 (const ODESystem &ode, const dictionary &dict) | |
Construct from ODESystem. More... | |
virtual | ~RKF45 () |
Destructor. More... | |
virtual bool | resize () |
Resize the ODE solver. More... | |
virtual scalar | solve (const scalar x0, const scalarField &y0, const label li, const scalarField &dydx0, const scalar dx, scalarField &y) const |
Solve a single step dx and return the error. More... | |
virtual void | solve (scalar &x, scalarField &y, const label li, 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... | |
ODESolver (const ODESolver &)=delete | |
Disallow default bitwise copy construction. More... | |
virtual | ~ODESolver () |
Destructor. More... | |
label | nEqns () const |
Return the number of equations to solve. More... | |
scalarField & | absTol () |
Return access to the absolute tolerance field. More... | |
scalarField & | relTol () |
Return access to the relative tolerance field. More... | |
template<class Type > | |
void | resizeField (UList< Type > &f) const |
void | resizeMatrix (scalarSquareMatrix &m) const |
virtual void | solve (scalar &x, scalarField &y, const label li, stepState &step) const |
Solve the ODE system from the current state xStart, y. More... | |
virtual void | solve (const scalar xStart, const scalar xEnd, scalarField &y, const label li, scalar &dxEst) const |
Solve the ODE system from the current state xStart, y. More... | |
void | operator= (const ODESolver &)=delete |
Disallow default bitwise assignment. More... | |
Public Member Functions inherited from adaptiveSolver | |
adaptiveSolver (const ODESystem &ode, const dictionary &dict) | |
Construct from ODESystem. More... | |
virtual | ~adaptiveSolver () |
Destructor. More... | |
bool | resize (const label n) |
Resize the ODE solver. More... | |
void | solve (const ODESystem &ode, scalar &x, scalarField &y, const label li, 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... | |
template<class Type > | |
static void | resizeField (UList< Type > &f, const label n) |
Protected Member Functions inherited from ODESolver | |
scalar | normalizeError (const scalarField &y0, const scalarField &y, const scalarField &err) const |
Return the normalized scalar error. More... | |
Protected Attributes inherited from ODESolver | |
const ODESystem & | odes_ |
Reference to ODESystem. More... | |
const label | maxN_ |
Maximum size of the ODESystem. More... | |
label | n_ |
Size of the ODESystem (adjustable) 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... | |
4/5th Order Runge-Kutta-Fehlberg ODE solver
Fehlberg, E. (1969). Low-order classical Runge-Kutta formulas with stepsize control and their application to some heat transfer problems. NASA Technical Report 315. Hairer, E., Nørsett, S. P., & Wanner, G. (1993). Solving Ordinary Differential Equations I: Nonstiff Problems, second edition. Springer-Verlag, Berlin.
This method embeds the 4-th order integration step into the 5-th order step and allows to perform an adaptive step-size control using these two order without the need of re-evaluation.
RKF45 | ( | const ODESystem & | ode, |
const dictionary & | dict | ||
) |
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inlinevirtual |
Destructor.
Definition at line 107 of file RKF45.H.
References RKF45::resize(), RKF45::solve(), ODESolver::solve(), x, y, and Foam::y0().
TypeName | ( | "RKF45" | ) |
Runtime type information.
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virtual |
Resize the ODE solver.
Implements ODESolver.
Definition at line 91 of file RKF45.C.
References ODESolver::n_, adaptiveSolver::resize(), ODESolver::resize(), ODESolver::resizeField(), and RKF45::solve().
Referenced by RKF45::~RKF45().
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virtual |
Solve a single step dx and return the error.
Implements adaptiveSolver.
Definition at line 115 of file RKF45.C.
References ODESystem::derivatives(), forAll, ODESolver::normalizeError(), and ODESolver::odes_.
Referenced by RKF45::resize(), and RKF45::~RKF45().
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virtual |
Solve the ODE system and the update the state.
Reimplemented from ODESolver.
Definition at line 184 of file RKF45.C.
References ODESolver::odes_, and adaptiveSolver::solve().