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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_RK4_HPP
#define VZ_RK4_HPP
namespace vZ
{
// RK4 method
//
// Fourth order Runge-Kutta method
// Four function evaluations per step
// Its tableau is:
//
// 0 |
// 1/2|1/2
// 1/2|0 1/2
// 1 |0 0 1
// ---+---------------
// |1/6 1/3 1/3 1/6
//
// k1 = dt*f(y[n])
// k2 = dt*f(y[n] + (dt/2)*k1)
// k3 = dt*f(y[n] + (dt/2)*k2)
// k4 = dt*f(y[n] + dt*k3)
// y[n + 1] = y[n] + (k1 + 2*k2 + 2*k3 + k4)/6
template <typename Y>
class GenericRK4Integrator : public GenericSimpleIntegrator<Y>
{
public:
typedef typename GenericSimpleIntegrator<Y>::Scalar Scalar;
typedef typename GenericSimpleIntegrator<Y>::Function Function;
GenericRK4Integrator(Function f)
: GenericSimpleIntegrator<Y>(f, s_a, s_b) { }
~GenericRK4Integrator() { }
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 Scalar s_a3Arr[2];
static Scalar s_a4Arr[3];
static std::vector<Scalar> s_aArr[3];
static Scalar s_bArr[4];
};
// Type alias
typedef GenericRK4Integrator<double> RK4Integrator;
// Implementation
template <typename Y>
typename GenericRK4Integrator<Y>::Scalar
GenericRK4Integrator<Y>::s_a2Arr[1] = {
Scalar(1)/Scalar(2)
};
template <typename Y>
typename GenericRK4Integrator<Y>::Scalar
GenericRK4Integrator<Y>::s_a3Arr[2] = {
Scalar(0), Scalar(1)/Scalar(2)
};
template <typename Y>
typename GenericRK4Integrator<Y>::Scalar
GenericRK4Integrator<Y>::s_a4Arr[3] = {
Scalar(0), Scalar(0), Scalar(1)
};
template <typename Y>
std::vector<typename GenericRK4Integrator<Y>::Scalar>
GenericRK4Integrator<Y>::s_aArr[3] = {
std::vector<Scalar>(s_a2Arr, s_a2Arr + 1),
std::vector<Scalar>(s_a3Arr, s_a3Arr + 2),
std::vector<Scalar>(s_a4Arr, s_a4Arr + 3)
};
template <typename Y>
typename GenericRK4Integrator<Y>::ACoefficients
GenericRK4Integrator<Y>::s_a(s_aArr, s_aArr + 3);
template <typename Y>
typename GenericRK4Integrator<Y>::Scalar
GenericRK4Integrator<Y>::s_bArr[4] = {
Scalar(1)/Scalar(6),
Scalar(1)/Scalar(3),
Scalar(1)/Scalar(3),
Scalar(1)/Scalar(6)
};
template <typename Y>
typename GenericRK4Integrator<Y>::BCoefficients
GenericRK4Integrator<Y>::s_b(s_bArr, s_bArr + 4);
}
#endif // VZ_RK4_HPP
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