RKF45.H

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License
    This file is part of OpenFOAM.

    OpenFOAM is free software: you can redistribute it and/or modify it
    under the terms of the GNU General Public License as published by
    the Free Software Foundation, either version 3 of the License, or
    (at your option) any later version.

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Class
    Foam::RKF45

Description
    4/5th Order Runge-Kutta-Fehlberg ODE solver

    References:
    \verbatim
        "Low-order classical Runge-Kutta formulas with step size control
         and their application to some heat transfer problems."
        Fehlberg, E.,
        NASA Technical Report 315, 1969.

        "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

    This method embedds the 4-th order integration step into the 5-th order step
    and allows to perform an adapdive step-size control using these two order
    without the need of re-evaluation.

SourceFiles
    RKF45.C

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

#ifndef RKF45_H
#define RKF45_H

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

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

namespace Foam
{

/*---------------------------------------------------------------------------*\
                           Class RKF45 Declaration
\*---------------------------------------------------------------------------*/

class RKF45
:
    public ODESolver,
    public adaptiveSolver
{
    // Private data

        //- RKF45 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, b5, 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("RKF45");


    // Constructors

        //- Construct from ODE
        RKF45(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

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