hub::integrator::Radau class
#include <src/integrator/Gauss-Radau.hpp>

Contents

Constant parameters used in Gauss Radau integration

https://www.cambridge.org/core/journals/international-astronomical-union-colloquium/article/an-efficient-integrator-that-uses-gauss-radau-spacings/F942BC9121C74CC2FA296050FC18D824

Public static functions

static auto h(size_t i) -> double constexpr
Substeps of Gauss-Radau stepping.
static auto rs(size_t n, size_t j) -> double constexpr
Coefficients used in 'g' update.
static auto rr(size_t n, size_t j) -> double constexpr
Coefficients used in 'g' update.
static auto est_b(size_t n, size_t j) -> double constexpr
Coefficient for B prediction update in equation 13.
static auto g2b(size_t n, size_t j) -> double constexpr
Transformation coefficients from G to B in equation 5.
static auto b2g(size_t n, size_t j) -> double constexpr
Transformation coefficients from B to G in equation 7.
static auto dy_tab(size_t stage, size_t i) -> double constexpr
Coefficients for y^ estimation in equation 10 after open the brackets.
template<typename Tab1, typename Tab2>
static void transform_g2b(Tab1 const& G, Tab2& B)
Calculate the corresponding B table from G table.
template<typename Tab1, typename Tab2>
static void transform_b2g(Tab1 const& B, Tab2& G)
Calculate the corresponding G table from B table.

Function documentation

static double hub::integrator::Radau::h(size_t i) constexpr

Substeps of Gauss-Radau stepping.

Parameters
i in Index of steps
Returns constexpr double

static double hub::integrator::Radau::rs(size_t n, size_t j) constexpr

Coefficients used in 'g' update.

Parameters
n in Raw index.
j in Column index
Returns constexpr double

Coefficients before G_i in equation 4 after open the brackets.

static double hub::integrator::Radau::rr(size_t n, size_t j) constexpr

Coefficients used in 'g' update.

Parameters
n in Raw index.
j in Column index
Returns constexpr double

Reciprocal of coefficient r_{ij} in equation 4.

static double hub::integrator::Radau::est_b(size_t n, size_t j) constexpr

Coefficient for B prediction update in equation 13.

Parameters
n in Raw index.
j in Column index.
Returns constexpr double

static double hub::integrator::Radau::g2b(size_t n, size_t j) constexpr

Transformation coefficients from G to B in equation 5.

Parameters
n in Raw index
j in Column index
Returns constexpr double

static double hub::integrator::Radau::b2g(size_t n, size_t j) constexpr

Transformation coefficients from B to G in equation 7.

Parameters
n in Raw index
j in Column index
Returns constexpr double

static double hub::integrator::Radau::dy_tab(size_t stage, size_t i) constexpr

Coefficients for y^ estimation in equation 10 after open the brackets.

Parameters
stage in Raw index(for x-th step)
i in Column index
Returns constexpr double

template<typename Tab1, typename Tab2>
static void hub::integrator::Radau::transform_g2b(Tab1 const& G, Tab2& B)

Calculate the corresponding B table from G table.

Template parameters
Tab1 Type of G table.
Tab2 Type of B table.
Parameters
G in G table.
B out B table.

template<typename Tab1, typename Tab2>
static void hub::integrator::Radau::transform_b2g(Tab1 const& B, Tab2& G)

Calculate the corresponding G table from B table.

Template parameters
Tab1 Type of B table.
Tab2 Type of G table.
Parameters
B in B table.
G out G table.