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/*************************************************************************
* Copyright (C) 2009-2010 Tavian Barnes <tavianator@gmail.com> *
* *
* This file is part of The vZ Library. *
* *
* The vZ Library is free software; you can redistribute it and/or *
* modify it under the terms of the GNU Lesser General Public License as *
* published by the Free Software Foundation; either version 3 of the *
* License, or (at your option) any later version. *
* *
* The vZ Library is distributed in the hope that it will be useful, but *
* WITHOUT ANY WARRANTY; without even the implied warranty of *
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU *
* Lesser General Public License for more details. *
* *
* You should have received a copy of the GNU Lesser General Public *
* License along with this program. If not, see *
* <http://www.gnu.org/licenses/>. *
*************************************************************************/
#ifndef VZ_MIDPOINT_HPP
#define VZ_MIDPOINT_HPP
namespace vZ
{
// Midpoint method
//
// Second order Runge-Kutta method
// Two function evaluations per step
// Its tableau is:
//
// 0 |
// 1/2|1/2
// ---+-----
// |0 1
//
// k1 = dt*f(y[n])
// k2 = dt*f(y[n] + (dt/2)*k1)
// y[n + 1] = y[n] + k2
template <typename Y>
class GenericMidpointIntegrator : public GenericSimpleIntegrator<Y>
{
public:
typedef typename GenericSimpleIntegrator<Y>::Scalar Scalar;
typedef typename GenericSimpleIntegrator<Y>::Function Function;
GenericMidpointIntegrator(Function f)
: GenericSimpleIntegrator<Y>(f, s_a, s_b) { }
~GenericMidpointIntegrator() { }
private:
typedef typename GenericSimpleIntegrator<Y>::ACoefficients ACoefficients;
typedef typename GenericSimpleIntegrator<Y>::BCoefficients BCoefficients;
static ACoefficients s_a;
static BCoefficients s_b;
static Scalar s_a2Arr[1];
static std::vector<Scalar> s_aArr[1];
static Scalar s_bArr[2];
};
// Type alias
typedef GenericMidpointIntegrator<double> MidpointIntegrator;
// Implementation
template <typename Y>
typename GenericMidpointIntegrator<Y>::Scalar
GenericMidpointIntegrator<Y>::s_a2Arr[1] = {
Scalar(1)/Scalar(2)
};
template <typename Y>
std::vector<typename GenericMidpointIntegrator<Y>::Scalar>
GenericMidpointIntegrator<Y>::s_aArr[1] = {
std::vector<Scalar>(s_a2Arr, s_a2Arr + 1)
};
template <typename Y>
typename GenericMidpointIntegrator<Y>::ACoefficients
GenericMidpointIntegrator<Y>::s_a(s_aArr, s_aArr + 1);
template <typename Y>
typename GenericMidpointIntegrator<Y>::Scalar
GenericMidpointIntegrator<Y>::s_bArr[2] = {
Scalar(0), Scalar(1)
};
template <typename Y>
typename GenericMidpointIntegrator<Y>::BCoefficients
GenericMidpointIntegrator<Y>::s_b(s_bArr, s_bArr + 2);
}
#endif // VZ_MIDPOINT_HPP
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