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specmicp/src/odeint/butcher_tableau.hpp
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butcher_tableau.hpp
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/*-------------------------------------------------------
- Module : odeint
- File : butcher_tableau.hpp
- Author : Fabien Georget
Copyright (c) 2014, Fabien Georget, Princeton University
---------------------------------------------------------*/
#ifndef SPECMICP_ODEINT_BUTCHERTABLEAU_HPP
#define SPECMICP_ODEINT_BUTCHERTABLEAU_HPP
//! \file butcher_tableau.hpp Butcher tableau for embedded runge kutta method
#include <array>
namespace specmicp {
namespace odeint {
template <int order, int s>
class ButcherTableau {
public:
static const int RK_order = order;
static const int RK_evaluations = s+1;
ButcherTableau(const std::array<double, s>& aa,
const std::array<std::array<double, s>, s>& ba,
const std::array<double, s+1>& ca,
const std::array<double, s+1>& csa
):
m_a(aa), m_b(ba), m_c(ca), m_cs(csa)
{}
ButcherTableau(std::array<double, s>&& aa,
std::array<std::array<double, s>, s>&& ba,
std::array<double, s+1>&& ca,
std::array<double, s+1>&& csa
):
m_a(aa), m_b(ba), m_c(ca), m_cs(csa)
{}
double a(int i) const {return m_a[i-2];}
double b(int i, int j) const {return m_b[i-2][j-1];}
double c(int i) const {return m_c[i-1];}
double cs(int i) const {return m_cs[i-1];}
private:
std::array<double, s> m_a;
std::array<std::array<double,s>, s> m_b;
std::array<double, s+1> m_c;
std::array<double, s+1> m_cs;
};
const ButcherTableau<5, 5> butcher_cash_karp45({1.0/5.0, 3.0/10.0, 3.0/5.0, 1.0, 7.0/8.0},
{{{1.0/5.0, 0, 0, 0, 0},
{3.0/40.0, 9.0/40.0, 0, 0, 0},
{3.0/10.0, -9.0/10.0, 6.0/5.0, 0, 0},
{-11.0/54.0, 5.0/2.0, -70.0/27.0, 35.0/27.0, 0},
{1631.0/55296.0, 175.0/512.0, 575.0/13824.0, 44275.0/110592.0, 253.0/4096.0}
}},
{37.0/378.0, 0.0, 250.0/621.0, 125.0/594.0, 0.0, 512.0/1771.0},
{2825.0/27648.0, 0.0, 18575.0/48384.0, 13525.0/55296.0, 277.0/14336.0, 1.0/4.0}
);
using ButcherTableauCashKarp_t = ButcherTableau<5, 5>;
const ButcherTableau<5, 6> butcher_dormand_prince45(
{1.0/5.0, 3.0/10.0, 4.0/5.0, 8.0/9.0, 1.0, 1.0},
{ {{1.0/5.0, 0, 0, 0, 0, 0},
{3.0/40.0, 9.0/40.0, 0, 0, 0, 0},
{44.0/45.0, -56.0/15.0, 32.0/9.0, 0, 0, 0},
{19372.0/6561.0, -25360.0/2187.0, 64448.0/6561.0, -212.0/729.0, 0, 0},
{9017.0/3168.0, -355.0/33.0, 46732.0/5247.0, 49.0/176.0, -5103.0/18656.0, 0},
{35.0/384.0, 0.0, 500.0/1113.0, 125.0/192.0, -2187.0/6784.0, 11.0/84.0}
}},
{35.0/384.0, 0.0, 500.0/1113.0, 125.0/192.0, -2187.0/6784.0, 11.0/84.0, 0.0},
{5179.0/57600.0, 0.0, 7571.0/16695.0, 393.0/640.0, -92097.0/339200.0, 187.0/2100.0, 1.0/40.0}
);
using ButcherTableauDormandPrince_t = ButcherTableau<5, 6>;
} // end namespace odeint
} // end namespace specmicp
#endif // SPECMICP_ODEINT_BUTCHERTABLEAU_HPP
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