GteOdeMidpoint.h

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// David Eberly, Geometric Tools, Redmond WA 98052
// Copyright (c) 1998-2017
// Distributed under the Boost Software License, Version 1.0.
// http://www.boost.org/LICENSE_1_0.txt
// http://www.geometrictools.com/License/Boost/LICENSE_1_0.txt
// File Version: 3.0.0 (2016/06/19)

#pragma once

#include <Mathematics/GteOdeSolver.h>

// The TVector template parameter allows you to create solvers with
// Vector<N,Real> when the dimension N is known at compile time or
// GVector<Real> when the dimension N is known at run time.  Both classes
// have 'int GetSize() const' that allow OdeSolver-derived classes to query
// for the dimension.

namespace gte
{

template <typename Real, typename TVector>
class OdeMidpoint : public OdeSolver<Real,TVector>
{
public:
    // Construction and destruction.
    virtual ~OdeMidpoint();
    OdeMidpoint(Real tDelta,
        std::function<TVector(Real, TVector const&)> const& F);

    // Estimate x(t + tDelta) from x(t) using dx/dt = F(t,x).  You may allow
    // xIn and xOut to be the same object.
    virtual void Update(Real tIn, TVector const& xIn, Real& tOut,
        TVector& xOut);
};


template <typename Real, typename TVector>
OdeMidpoint<Real, TVector>::~OdeMidpoint()
{
}

template <typename Real, typename TVector>
OdeMidpoint<Real, TVector>::OdeMidpoint(Real tDelta,
    std::function<TVector(Real, TVector const&)> const& F)
    :
    OdeSolver<Real, TVector>(tDelta, F)
{
}

template <typename Real, typename TVector>
void OdeMidpoint<Real, TVector>::Update(Real tIn, TVector const& xIn,
    Real& tOut, TVector& xOut)
{
    // Compute the first step.
    Real halfTDelta = ((Real)0.5) * this->mTDelta;
    TVector fVector = this->mFunction(tIn, xIn);
    TVector xTemp = xIn + halfTDelta * fVector;

    // Compute the second step.
    Real halfT = tIn + halfTDelta;
    fVector = this->mFunction(halfT, xTemp);
    tOut = tIn + this->mTDelta;
    xOut = xIn + this->mTDelta * fVector;
}


}