RKCK45.H

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License
    This file is part of OpenFOAM.

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    the Free Software Foundation, either version 3 of the License, or
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Class
    Foam::RKCK45

Description
    4/5th Order Cash-Karp Runge-Kutta ODE solver.

    References:
    \verbatim
        "A variable order Runge-Kutta method for initial value problems
         with rapidly varying right-hand sides"
        Cash, J.R.,
        Karp, A.H.
        ACM Transactions on Mathematical Software, vol. 16, 1990, pp. 201–222.

        "Solving Ordinary Differential Equations I: Nonstiff Problems,
         second edition",
        Hairer, E.,
        Nørsett, S.,
        Wanner, G.,
        Springer-Verlag, Berlin. 1993, ISBN 3-540-56670-8.
    \endverbatim

SourceFiles
    RKCK45.C

\*---------------------------------------------------------------------------*/

#ifndef RKCK45_H
#define RKCK45_H

#include "ODESolver.H"
#include "adaptiveSolver.H"

// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //

namespace Foam
{

/*---------------------------------------------------------------------------*\
                           Class RKCK45 Declaration
\*---------------------------------------------------------------------------*/

class RKCK45
:
    public ODESolver,
    public adaptiveSolver
{
    // Private data

        //- RKCK Constants
        static const scalar
            c2, c3, c4, c5, c6,
            a21, a31, a32, a41, a42, a43, a51, a52, a53, a54,
            a61, a62, a63, a64, a65,
            b1, b3, b4, b6,
            e1, e3, e4, e5, e6;

        // Temporary fields
        mutable scalarField yTemp_;
        mutable scalarField k2_;
        mutable scalarField k3_;
        mutable scalarField k4_;
        mutable scalarField k5_;
        mutable scalarField k6_;

        //- Error-estimate field
        mutable scalarField err_;


public:

    //- Runtime type information
    TypeName("RKCK45");


    // Constructors

        //- Construct from ODE
        RKCK45(const ODESystem& ode, const dictionary& dict);


    // Member Functions

        //- Inherit solve from ODESolver
        using ODESolver::solve;

        //- Solve a single step dx and return the error
        scalar solve
        (
            const scalar x0,
            const scalarField& y0,
            const scalarField& dydx0,
            const scalar dx,
            scalarField& y
        ) const;

        //- Solve the ODE system and the update the state
        void solve
        (
            scalar& x,
            scalarField& y,
            scalar& dxTry
        ) const;
};


// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //

} // End namespace Foam

// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //

#endif

// ************************************************************************* //