Class of Tanaka Formula 2. More...

#include <num_collect/ode/runge_kutta/tanaka2_formula.h>

Inheritance diagram for num_collect::ode::runge_kutta::tanaka2_formula< Problem, FormulaSolver >:

Collaboration diagram for num_collect::ode::runge_kutta::tanaka2_formula< Problem, FormulaSolver >:

Public Types
using	base_type
	Type of base class.

using	problem_type
	Type of problem.

using	scalar_type
	Type of scalars.

using	this_type = tanaka2_formula<Problem, FormulaSolver>
	Type of this class.

using	variable_type
	Type of variables.

Public Types inherited from num_collect::ode::runge_kutta::implicit_formula_base< Derived, Problem, FormulaSolver >
using	base_type = formula_base<Derived, Problem>
	Type of base class.

using	formula_solver_type = FormulaSolver
	Type of solver of formula.

using	problem_type
	Type of problem.

using	scalar_type
	Type of scalars.

using	variable_type
	Type of variables.

Public Types inherited from num_collect::ode::formula_base< Derived, Problem >
using	problem_type = Problem
	Type of problem.

using	scalar_type = typename problem_type::scalar_type
	Type of scalars.

using	variable_type = typename problem_type::variable_type
	Type of variables.

Public Member Functions
void	step (scalar_type time, scalar_type step_size, const variable_type &current, variable_type &estimate)
	Compute the next variable.

void	step_embedded (scalar_type time, scalar_type step_size, const variable_type &current, variable_type &estimate, variable_type &error)
	Compute the next variable and weak estimate of it with embedded formula.

Public Member Functions inherited from num_collect::ode::runge_kutta::implicit_formula_base< Derived, Problem, FormulaSolver >
	implicit_formula_base (const problem_type &problem=problem_type())
	Constructor.

auto	formula_solver () -> formula_solver_type &
	Get solver of formula.

auto	formula_solver () const -> const formula_solver_type &
	Get solver of formula.

auto	logger () const noexcept -> const num_collect::logging::logger &
	Access to the logger.

auto	logger () noexcept -> num_collect::logging::logger &
	Access to the logger.

auto	tolerances (const error_tolerances< variable_type > &val) -> Derived &
	Set the error tolerances.

Public Member Functions inherited from num_collect::ode::formula_base< Derived, Problem >
	formula_base (const problem_type &problem=problem_type())
	Constructor.

auto	problem () -> problem_type &
	Get the problem.

auto	problem () const -> const problem_type &
	Get the problem.

void	step (scalar_type time, scalar_type step_size, const variable_type &current, variable_type &estimate)
	Compute the next variable.

Static Public Attributes
static constexpr index_type	lesser_order = 2
	Order of lesser coefficients of this formula.

static constexpr auto	log_tag
	Log tag.

static constexpr index_type	order = 4
	Order of this formula.

static constexpr index_type	stages = 3
	Number of stages of this formula.

Coefficients in Butcher array.
`a` is coefficients of intermidiate variables in calculation of intermidiate variables. `b` is coefficients of time in calculation of intermidiate variables. `c` is coefficients of intermidiate variables in calculation of estimates of next variables.
static constexpr scalar_type	a11 = coeff(133, 100)

static constexpr scalar_type	a21 = coeff(-5400, 18167)

static constexpr scalar_type	a22 = coeff(28967, 36334)

static constexpr scalar_type	a31 = coeff(133, 50)

static constexpr scalar_type	a32 = coeff(-108, 25)

static constexpr scalar_type	a33 = coeff(133, 100)

static constexpr scalar_type	b1 = coeff(133, 100)

static constexpr scalar_type	b2 = coeff(1, 2)

static constexpr scalar_type	b3 = coeff(-33, 100)

static constexpr scalar_type	c1 = coeff(1250, 20667)

static constexpr scalar_type	c2 = coeff(18167, 20667)

static constexpr scalar_type	c3 = coeff(1250, 20667)

static constexpr scalar_type	cw2 = coeff(1)

static constexpr scalar_type	ce1 = c1

static constexpr scalar_type	ce2 = c2 - cw2

static constexpr scalar_type	ce3 = c3

Protected Member Functions
auto	formula_solver () -> formula_solver_type &
	Get solver of formula.

auto	formula_solver () const -> const formula_solver_type &
	Get solver of formula.

Protected Member Functions inherited from num_collect::ode::runge_kutta::implicit_formula_base< Derived, Problem, FormulaSolver >
auto	derived () const noexcept -> const Derived &
	Access derived object.

auto	derived () noexcept -> Derived &
	Access derived object.

Protected Member Functions inherited from num_collect::ode::formula_base< Derived, Problem >
auto	derived () const noexcept -> const Derived &
	Access derived object.

auto	derived () noexcept -> Derived &
	Access derived object.

Private Attributes
Intermediate variables.
variable_type	k1_ {}

variable_type	k2_ {}

variable_type	k3_ {}

Additional Inherited Members
Static Protected Member Functions inherited from num_collect::ode::formula_base< Derived, Problem >
template<typename T >
static constexpr auto	coeff (T val) -> scalar_type
	Convert coefficients.

template<typename T1 , typename T2 >
static constexpr auto	coeff (T1 num, T2 den) -> scalar_type
	Create coefficients.

Detailed Description

template<concepts::problem Problem, concepts::slope_equation_solver FormulaSolver = inexact_newton_slope_equation_solver<Problem>>
class num_collect::ode::runge_kutta::tanaka2_formula< Problem, FormulaSolver >

Class of Tanaka Formula 2.

Template Parameters

Problem	Type of problem.
FormulaSolver	Type of solver of formula.

Definition at line 41 of file tanaka2_formula.h.

Member Typedef Documentation

◆ base_type

template<concepts::problem Problem, concepts::slope_equation_solver FormulaSolver = inexact_newton_slope_equation_solver<Problem>>

using num_collect::ode::runge_kutta::tanaka2_formula< Problem, FormulaSolver >::base_type

Initial value:

 
        implicit_formula_base<tanaka2_formula<Problem, FormulaSolver>, Problem,
            FormulaSolver>

Type of base class.

Definition at line 49 of file tanaka2_formula.h.

◆ problem_type

template<concepts::problem Problem, concepts::slope_equation_solver FormulaSolver = inexact_newton_slope_equation_solver<Problem>>

using num_collect::ode::formula_base< Derived, Problem >::problem_type

Type of problem.

Definition at line 44 of file formula_base.h.

◆ scalar_type

template<concepts::problem Problem, concepts::slope_equation_solver FormulaSolver = inexact_newton_slope_equation_solver<Problem>>

using num_collect::ode::formula_base< Derived, Problem >::scalar_type

Type of scalars.

Definition at line 45 of file formula_base.h.

◆ this_type

template<concepts::problem Problem, concepts::slope_equation_solver FormulaSolver = inexact_newton_slope_equation_solver<Problem>>

using num_collect::ode::runge_kutta::tanaka2_formula< Problem, FormulaSolver >::this_type = tanaka2_formula<Problem, FormulaSolver>

Type of this class.

Definition at line 46 of file tanaka2_formula.h.

◆ variable_type

template<concepts::problem Problem, concepts::slope_equation_solver FormulaSolver = inexact_newton_slope_equation_solver<Problem>>

using num_collect::ode::formula_base< Derived, Problem >::variable_type

Type of variables.

Definition at line 46 of file formula_base.h.

Member Function Documentation

◆ formula_solver() [1/2]

template<concepts::problem Problem, concepts::slope_equation_solver FormulaSolver = inexact_newton_slope_equation_solver<Problem>>

auto num_collect::ode::runge_kutta::implicit_formula_base< Derived, Problem, FormulaSolver >::formula_solver ( ) -> formula_solver_type&

inlinenodiscardprotected

Get solver of formula.

Returns: Solver of formula.

Definition at line 68 of file implicit_formula_base.h.

◆ formula_solver() [2/2]

template<concepts::problem Problem, concepts::slope_equation_solver FormulaSolver = inexact_newton_slope_equation_solver<Problem>>

auto num_collect::ode::runge_kutta::implicit_formula_base< Derived, Problem, FormulaSolver >::formula_solver ( ) const -> const formula_solver_type&

inlinenodiscardprotected

Get solver of formula.

Returns: Solver of formula.

Definition at line 77 of file implicit_formula_base.h.

◆ step()

template<concepts::problem Problem, concepts::slope_equation_solver FormulaSolver = inexact_newton_slope_equation_solver<Problem>>

void num_collect::ode::runge_kutta::tanaka2_formula< Problem, FormulaSolver >::step	(	scalar_type	time,
		scalar_type	step_size,
		const variable_type &	current,
		variable_type &	estimate )

inline

Compute the next variable.

Parameters

[in]	time	Current time.
[in]	step_size	Step size.
[in]	current	Current variable.
[out]	estimate	Estimate of the next variable.

Definition at line 115 of file tanaka2_formula.h.

◆ step_embedded()

template<concepts::problem Problem, concepts::slope_equation_solver FormulaSolver = inexact_newton_slope_equation_solver<Problem>>

void num_collect::ode::runge_kutta::tanaka2_formula< Problem, FormulaSolver >::step_embedded	(	scalar_type	time,
		scalar_type	step_size,
		const variable_type &	current,
		variable_type &	estimate,
		variable_type &	error )

inline

Compute the next variable and weak estimate of it with embedded formula.

Parameters

[in]	time	Current time.
[in]	step_size	Step size.
[in]	current	Current variable.
[out]	estimate	Estimate of the next variable.
[out]	error	Estimate of error.

Definition at line 131 of file tanaka2_formula.h.

Member Data Documentation

◆ a11

template<concepts::problem Problem, concepts::slope_equation_solver FormulaSolver = inexact_newton_slope_equation_solver<Problem>>

scalar_type num_collect::ode::runge_kutta::tanaka2_formula< Problem, FormulaSolver >::a11 = coeff(133, 100)

staticconstexpr

Coefficient in Butcher array.

Definition at line 92 of file tanaka2_formula.h.

◆ a21

template<concepts::problem Problem, concepts::slope_equation_solver FormulaSolver = inexact_newton_slope_equation_solver<Problem>>

scalar_type num_collect::ode::runge_kutta::tanaka2_formula< Problem, FormulaSolver >::a21 = coeff(-5400, 18167)

staticconstexpr

Coefficient in Butcher array.

Definition at line 93 of file tanaka2_formula.h.

◆ a22

template<concepts::problem Problem, concepts::slope_equation_solver FormulaSolver = inexact_newton_slope_equation_solver<Problem>>

scalar_type num_collect::ode::runge_kutta::tanaka2_formula< Problem, FormulaSolver >::a22 = coeff(28967, 36334)

staticconstexpr

Coefficient in Butcher array.

Definition at line 94 of file tanaka2_formula.h.

◆ a31

template<concepts::problem Problem, concepts::slope_equation_solver FormulaSolver = inexact_newton_slope_equation_solver<Problem>>

scalar_type num_collect::ode::runge_kutta::tanaka2_formula< Problem, FormulaSolver >::a31 = coeff(133, 50)

staticconstexpr

Coefficient in Butcher array.

Definition at line 95 of file tanaka2_formula.h.

◆ a32

template<concepts::problem Problem, concepts::slope_equation_solver FormulaSolver = inexact_newton_slope_equation_solver<Problem>>

scalar_type num_collect::ode::runge_kutta::tanaka2_formula< Problem, FormulaSolver >::a32 = coeff(-108, 25)

staticconstexpr

Coefficient in Butcher array.

Definition at line 96 of file tanaka2_formula.h.

◆ a33

template<concepts::problem Problem, concepts::slope_equation_solver FormulaSolver = inexact_newton_slope_equation_solver<Problem>>

scalar_type num_collect::ode::runge_kutta::tanaka2_formula< Problem, FormulaSolver >::a33 = coeff(133, 100)

staticconstexpr

Coefficient in Butcher array.

Definition at line 97 of file tanaka2_formula.h.

◆ b1

template<concepts::problem Problem, concepts::slope_equation_solver FormulaSolver = inexact_newton_slope_equation_solver<Problem>>

scalar_type num_collect::ode::runge_kutta::tanaka2_formula< Problem, FormulaSolver >::b1 = coeff(133, 100)

staticconstexpr

Coefficient in Butcher array.

Definition at line 99 of file tanaka2_formula.h.

◆ b2

template<concepts::problem Problem, concepts::slope_equation_solver FormulaSolver = inexact_newton_slope_equation_solver<Problem>>

scalar_type num_collect::ode::runge_kutta::tanaka2_formula< Problem, FormulaSolver >::b2 = coeff(1, 2)

staticconstexpr

Coefficient in Butcher array.

Definition at line 100 of file tanaka2_formula.h.

◆ b3

template<concepts::problem Problem, concepts::slope_equation_solver FormulaSolver = inexact_newton_slope_equation_solver<Problem>>

scalar_type num_collect::ode::runge_kutta::tanaka2_formula< Problem, FormulaSolver >::b3 = coeff(-33, 100)

staticconstexpr

Coefficient in Butcher array.

Definition at line 101 of file tanaka2_formula.h.

◆ c1

template<concepts::problem Problem, concepts::slope_equation_solver FormulaSolver = inexact_newton_slope_equation_solver<Problem>>

scalar_type num_collect::ode::runge_kutta::tanaka2_formula< Problem, FormulaSolver >::c1 = coeff(1250, 20667)

staticconstexpr

Coefficient in Butcher array.

Definition at line 103 of file tanaka2_formula.h.

◆ c2

template<concepts::problem Problem, concepts::slope_equation_solver FormulaSolver = inexact_newton_slope_equation_solver<Problem>>

scalar_type num_collect::ode::runge_kutta::tanaka2_formula< Problem, FormulaSolver >::c2 = coeff(18167, 20667)

staticconstexpr

Coefficient in Butcher array.

Definition at line 104 of file tanaka2_formula.h.

◆ c3

template<concepts::problem Problem, concepts::slope_equation_solver FormulaSolver = inexact_newton_slope_equation_solver<Problem>>

scalar_type num_collect::ode::runge_kutta::tanaka2_formula< Problem, FormulaSolver >::c3 = coeff(1250, 20667)

staticconstexpr

Coefficient in Butcher array.

Definition at line 105 of file tanaka2_formula.h.

◆ ce1

template<concepts::problem Problem, concepts::slope_equation_solver FormulaSolver = inexact_newton_slope_equation_solver<Problem>>

scalar_type num_collect::ode::runge_kutta::tanaka2_formula< Problem, FormulaSolver >::ce1 = c1

staticconstexpr

Coefficient in Butcher array.

Definition at line 109 of file tanaka2_formula.h.

◆ ce2

template<concepts::problem Problem, concepts::slope_equation_solver FormulaSolver = inexact_newton_slope_equation_solver<Problem>>

scalar_type num_collect::ode::runge_kutta::tanaka2_formula< Problem, FormulaSolver >::ce2 = c2 - cw2

staticconstexpr

Coefficient in Butcher array.

Definition at line 110 of file tanaka2_formula.h.

◆ ce3

template<concepts::problem Problem, concepts::slope_equation_solver FormulaSolver = inexact_newton_slope_equation_solver<Problem>>

scalar_type num_collect::ode::runge_kutta::tanaka2_formula< Problem, FormulaSolver >::ce3 = c3

staticconstexpr

Coefficient in Butcher array.

Definition at line 111 of file tanaka2_formula.h.

◆ cw2

template<concepts::problem Problem, concepts::slope_equation_solver FormulaSolver = inexact_newton_slope_equation_solver<Problem>>

scalar_type num_collect::ode::runge_kutta::tanaka2_formula< Problem, FormulaSolver >::cw2 = coeff(1)

staticconstexpr

Coefficient in Butcher array.

Definition at line 107 of file tanaka2_formula.h.

◆ k1_

template<concepts::problem Problem, concepts::slope_equation_solver FormulaSolver = inexact_newton_slope_equation_solver<Problem>>

variable_type num_collect::ode::runge_kutta::tanaka2_formula< Problem, FormulaSolver >::k1_ {}

private

Intermediate variable.

Definition at line 162 of file tanaka2_formula.h.

◆ k2_

template<concepts::problem Problem, concepts::slope_equation_solver FormulaSolver = inexact_newton_slope_equation_solver<Problem>>

variable_type num_collect::ode::runge_kutta::tanaka2_formula< Problem, FormulaSolver >::k2_ {}

private

Intermediate variable.

Definition at line 163 of file tanaka2_formula.h.

◆ k3_

template<concepts::problem Problem, concepts::slope_equation_solver FormulaSolver = inexact_newton_slope_equation_solver<Problem>>

variable_type num_collect::ode::runge_kutta::tanaka2_formula< Problem, FormulaSolver >::k3_ {}

private

Intermediate variable.

Definition at line 164 of file tanaka2_formula.h.

◆ lesser_order

template<concepts::problem Problem, concepts::slope_equation_solver FormulaSolver = inexact_newton_slope_equation_solver<Problem>>

index_type num_collect::ode::runge_kutta::tanaka2_formula< Problem, FormulaSolver >::lesser_order = 2

staticconstexpr

Order of lesser coefficients of this formula.

Definition at line 75 of file tanaka2_formula.h.

◆ log_tag

template<concepts::problem Problem, concepts::slope_equation_solver FormulaSolver = inexact_newton_slope_equation_solver<Problem>>

auto num_collect::ode::runge_kutta::tanaka2_formula< Problem, FormulaSolver >::log_tag

staticconstexpr

Initial value:

=

logging::log_tag_view("num_collect::ode::runge_kutta::tanaka2_formula")

Log tag.

Definition at line 78 of file tanaka2_formula.h.

◆ order

template<concepts::problem Problem, concepts::slope_equation_solver FormulaSolver = inexact_newton_slope_equation_solver<Problem>>

index_type num_collect::ode::runge_kutta::tanaka2_formula< Problem, FormulaSolver >::order = 4

staticconstexpr

Order of this formula.

Definition at line 72 of file tanaka2_formula.h.

◆ stages

template<concepts::problem Problem, concepts::slope_equation_solver FormulaSolver = inexact_newton_slope_equation_solver<Problem>>

index_type num_collect::ode::runge_kutta::tanaka2_formula< Problem, FormulaSolver >::stages = 3

staticconstexpr

Number of stages of this formula.

Definition at line 69 of file tanaka2_formula.h.

The documentation for this class was generated from the following file:

include/num_collect/ode/runge_kutta/tanaka2_formula.h

Public Types

Public Member Functions

Static Public Attributes

Protected Member Functions

Private Attributes

Additional Inherited Members

Detailed Description

Member Typedef Documentation

◆ base_type

◆ problem_type

◆ scalar_type

◆ this_type

◆ variable_type

Member Function Documentation

◆ formula_solver() [1/2]

◆ formula_solver() [2/2]

◆ step()

◆ step_embedded()

Member Data Documentation

◆ a11

◆ a21

◆ a22

◆ a31

◆ a32

◆ a33

◆ b1

◆ b2

◆ b3

◆ c1

◆ c2

◆ c3

◆ ce1

◆ ce2

◆ ce3

◆ cw2

◆ k1_

◆ k2_

◆ k3_

◆ lesser_order

◆ log_tag

◆ order

◆ stages