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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_BS23_HPP
#define VZ_BS23_HPP
namespace vZ
{
// Bogacki-Shampine method
//
// Third-order with embedded second-order
// Its tableau is:
//
// 0 |
// 1/2 | 1/2
// 3/4 | 0 3/4
// 1 | 2/9 1/3 4/9
// ----+-----------------
// b | 2/9 1/3 4/9 0
// b* | 7/24 1/4 1/3 1/8
template <typename Y>
class GenericBS23Integrator : public GenericAdaptiveIntegrator<Y>
{
public:
typedef typename GenericAdaptiveIntegrator<Y>::Scalar Scalar;
typedef typename GenericAdaptiveIntegrator<Y>::Function Function;
GenericBS23Integrator(Function f)
: GenericAdaptiveIntegrator<Y>(f, 3, s_a, s_b, s_bStar) { }
~GenericBS23Integrator() { }
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 Scalar s_a3Arr[2];
static Scalar s_a4Arr[3];
static std::vector<Scalar> s_aArr[3];
static Scalar s_bArr[4];
static Scalar s_bStarArr[4];
};
// Type alias
typedef GenericBS23Integrator<double> BS23Integrator;
// Implementation
template <typename Y>
typename GenericBS23Integrator<Y>::Scalar
GenericBS23Integrator<Y>::s_a2Arr[1] = {
Scalar(1)/Scalar(2)
};
template <typename Y>
typename GenericBS23Integrator<Y>::Scalar
GenericBS23Integrator<Y>::s_a3Arr[2] = {
Scalar(0), Scalar(3)/Scalar(4)
};
template <typename Y>
typename GenericBS23Integrator<Y>::Scalar
GenericBS23Integrator<Y>::s_a4Arr[3] = {
Scalar(2)/Scalar(9), Scalar(1)/Scalar(3), Scalar(4)/Scalar(9)
};
template <typename Y>
std::vector<typename GenericBS23Integrator<Y>::Scalar>
GenericBS23Integrator<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 GenericBS23Integrator<Y>::ACoefficients
GenericBS23Integrator<Y>::s_a(s_aArr, s_aArr + 3);
template <typename Y>
typename GenericBS23Integrator<Y>::Scalar
GenericBS23Integrator<Y>::s_bArr[4] = {
Scalar(2)/Scalar(9),
Scalar(1)/Scalar(3),
Scalar(4)/Scalar(9),
Scalar(0)
};
template <typename Y>
typename GenericBS23Integrator<Y>::BCoefficients
GenericBS23Integrator<Y>::s_b(s_bArr, s_bArr + 4);
template <typename Y>
typename GenericBS23Integrator<Y>::Scalar
GenericBS23Integrator<Y>::s_bStarArr[4] = {
Scalar(7)/Scalar(24),
Scalar(1)/Scalar(4),
Scalar(1)/Scalar(3),
Scalar(1)/Scalar(8)
};
template <typename Y>
typename GenericBS23Integrator<Y>::BCoefficients
GenericBS23Integrator<Y>::s_bStar(s_bStarArr, s_bStarArr + 4);
}
#endif // VZ_BS23_HPP
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