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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_HE12_HPP
#define VZ_HE12_HPP
namespace vZ
{
// Heun-Euler method
//
// Second-order with embedded first-order
// Its tableau is:
//
// 0 |
// 1 | 1
// ---+---------
// b | 1/2 1/2
// b* | 1 0
template <typename Y>
class GenericHE12Integrator : public GenericAdaptiveIntegrator<Y>
{
public:
typedef typename GenericAdaptiveIntegrator<Y>::Scalar Scalar;
typedef typename GenericAdaptiveIntegrator<Y>::Function Function;
GenericHE12Integrator(Function f)
: GenericAdaptiveIntegrator<Y>(f, 2, s_a, s_b, s_bStar) { }
~GenericHE12Integrator() { }
private:
typedef typename GenericAdaptiveIntegrator<Y>::ACoefficients ACoefficients;
typedef typename GenericAdaptiveIntegrator<Y>::BCoefficients BCoefficients;
static ACoefficients s_a;
static BCoefficients s_b;
static BCoefficients s_bStar;
static Scalar s_a2Arr[1];
static std::vector<Scalar> s_aArr[1];
static Scalar s_bArr[2];
static Scalar s_bStarArr[2];
};
// Type alias
typedef GenericHE12Integrator<double> HE12Integrator;
// Implementation
template <typename Y>
typename GenericHE12Integrator<Y>::Scalar
GenericHE12Integrator<Y>::s_a2Arr[1] = {
Scalar(1)
};
template <typename Y>
std::vector<typename GenericHE12Integrator<Y>::Scalar>
GenericHE12Integrator<Y>::s_aArr[1] = {
std::vector<Scalar>(s_a2Arr, s_a2Arr + 1)
};
template <typename Y>
typename GenericHE12Integrator<Y>::ACoefficients
GenericHE12Integrator<Y>::s_a(s_aArr, s_aArr + 1);
template <typename Y>
typename GenericHE12Integrator<Y>::Scalar
GenericHE12Integrator<Y>::s_bArr[2] = {
Scalar(1)/Scalar(2), Scalar(1)/Scalar(2)
};
template <typename Y>
typename GenericHE12Integrator<Y>::BCoefficients
GenericHE12Integrator<Y>::s_b(s_bArr, s_bArr + 2);
template <typename Y>
typename GenericHE12Integrator<Y>::Scalar
GenericHE12Integrator<Y>::s_bStarArr[2] = {
Scalar(1), Scalar(0)
};
template <typename Y>
typename GenericHE12Integrator<Y>::BCoefficients
GenericHE12Integrator<Y>::s_bStar(s_bStarArr, s_bStarArr + 2);
}
#endif // VZ_HE12_HPP
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