Class of Runge-Kutta-Fehlberg 45 formula. More...

#include <num_collect/ode/runge_kutta/rkf45_formula.h>

Inheritance diagram for num_collect::ode::runge_kutta::rkf45_formula< Problem >:

Collaboration diagram for num_collect::ode::runge_kutta::rkf45_formula< Problem >:

Public Types
using	base_type = formula_base<rkf45_formula<Problem>, Problem>
	Type of base class.

Public Types inherited from num_collect::ode::formula_base< rkf45_formula< Problem >, Problem >
using	problem_type
	Type of problem.

using	scalar_type
	Type of scalars.

using	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::formula_base< rkf45_formula< Problem >, 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 = 4
	Order of lesser coefficients of this formula.

static constexpr auto	log_tag
	Log tag.

static constexpr index_type	order = 5
	Order of this formula.

static constexpr index_type	stages = 6
	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	a21 = coeff(1, 4)

static constexpr scalar_type	a31 = coeff(3, 32)

static constexpr scalar_type	a32 = coeff(9, 32)

static constexpr scalar_type	a41 = coeff(1932, 2197)

static constexpr scalar_type	a42 = coeff(-7200, 2197)

static constexpr scalar_type	a43 = coeff(7296, 2197)

static constexpr scalar_type	a51 = coeff(439, 216)

static constexpr scalar_type	a52 = coeff(-8)

static constexpr scalar_type	a53 = coeff(3680, 513)

static constexpr scalar_type	a54 = coeff(-845, 4104)

static constexpr scalar_type	a61 = coeff(-8, 27)

static constexpr scalar_type	a62 = coeff(2)

static constexpr scalar_type	a63 = coeff(-3544, 2565)

static constexpr scalar_type	a64 = coeff(1859, 4104)

static constexpr scalar_type	a65 = coeff(-11, 40)

static constexpr scalar_type	b2 = coeff(1, 4)

static constexpr scalar_type	b3 = coeff(3, 8)

static constexpr scalar_type	b4 = coeff(12, 13)

static constexpr scalar_type	b5 = coeff(1)

static constexpr scalar_type	b6 = coeff(1, 2)

static constexpr scalar_type	c1 = coeff(16, 135)

static constexpr scalar_type	c3 = coeff(6656, 12825)

static constexpr scalar_type	c4 = coeff(28561, 56430)

static constexpr scalar_type	c5 = coeff(-9, 50)

static constexpr scalar_type	c6 = coeff(2, 55)

static constexpr scalar_type	cw1 = coeff(25, 216)

static constexpr scalar_type	cw3 = coeff(1408, 2565)

static constexpr scalar_type	cw4 = coeff(2197, 4104)

static constexpr scalar_type	cw5 = coeff(-1, 5)

static constexpr scalar_type	ce1 = c1 - cw1

static constexpr scalar_type	ce3 = c3 - cw3

static constexpr scalar_type	ce4 = c4 - cw4

static constexpr scalar_type	ce5 = c5 - cw5

static constexpr scalar_type	ce6 = c6

Private Attributes
Intermediate variables.
variable_type	k1_ {}

variable_type	k2_ {}

variable_type	k3_ {}

variable_type	k4_ {}

variable_type	k5_ {}

variable_type	k6_ {}

Additional Inherited Members
Protected Member Functions inherited from num_collect::ode::formula_base< rkf45_formula< Problem >, Problem >
auto	derived () const noexcept -> const rkf45_formula< Problem > &
	Access derived object.

auto	derived () noexcept -> rkf45_formula< Problem > &
	Access derived object.

Static Protected Member Functions inherited from num_collect::ode::formula_base< rkf45_formula< Problem >, Problem >
static constexpr auto	coeff (T val) -> scalar_type
	Convert coefficients.

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

Detailed Description

template<concepts::problem Problem>
class num_collect::ode::runge_kutta::rkf45_formula< Problem >

Class of Runge-Kutta-Fehlberg 45 formula.

Template Parameters

Problem Type of problem.

Definition at line 37 of file rkf45_formula.h.

Member Typedef Documentation

◆ base_type

template<concepts::problem Problem>

using num_collect::ode::runge_kutta::rkf45_formula< Problem >::base_type = formula_base<rkf45_formula<Problem>, Problem>

Type of base class.

Definition at line 40 of file rkf45_formula.h.

Member Function Documentation

◆ step()

template<concepts::problem Problem>

void num_collect::ode::runge_kutta::rkf45_formula< Problem >::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 121 of file rkf45_formula.h.

◆ step_embedded()

template<concepts::problem Problem>

void num_collect::ode::runge_kutta::rkf45_formula< Problem >::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 137 of file rkf45_formula.h.

Member Data Documentation

◆ a21

template<concepts::problem Problem>

scalar_type num_collect::ode::runge_kutta::rkf45_formula< Problem >::a21 = coeff(1, 4)

staticconstexpr

Coefficient in Butcher array.

Definition at line 80 of file rkf45_formula.h.

◆ a31

template<concepts::problem Problem>

scalar_type num_collect::ode::runge_kutta::rkf45_formula< Problem >::a31 = coeff(3, 32)

staticconstexpr

Coefficient in Butcher array.

Definition at line 81 of file rkf45_formula.h.

◆ a32

template<concepts::problem Problem>

scalar_type num_collect::ode::runge_kutta::rkf45_formula< Problem >::a32 = coeff(9, 32)

staticconstexpr

Coefficient in Butcher array.

Definition at line 82 of file rkf45_formula.h.

◆ a41

template<concepts::problem Problem>

scalar_type num_collect::ode::runge_kutta::rkf45_formula< Problem >::a41 = coeff(1932, 2197)

staticconstexpr

Coefficient in Butcher array.

Definition at line 83 of file rkf45_formula.h.

◆ a42

template<concepts::problem Problem>

scalar_type num_collect::ode::runge_kutta::rkf45_formula< Problem >::a42 = coeff(-7200, 2197)

staticconstexpr

Coefficient in Butcher array.

Definition at line 84 of file rkf45_formula.h.

◆ a43

template<concepts::problem Problem>

scalar_type num_collect::ode::runge_kutta::rkf45_formula< Problem >::a43 = coeff(7296, 2197)

staticconstexpr

Coefficient in Butcher array.

Definition at line 85 of file rkf45_formula.h.

◆ a51

template<concepts::problem Problem>

scalar_type num_collect::ode::runge_kutta::rkf45_formula< Problem >::a51 = coeff(439, 216)

staticconstexpr

Coefficient in Butcher array.

Definition at line 86 of file rkf45_formula.h.

◆ a52

template<concepts::problem Problem>

scalar_type num_collect::ode::runge_kutta::rkf45_formula< Problem >::a52 = coeff(-8)

staticconstexpr

Coefficient in Butcher array.

Definition at line 87 of file rkf45_formula.h.

◆ a53

template<concepts::problem Problem>

scalar_type num_collect::ode::runge_kutta::rkf45_formula< Problem >::a53 = coeff(3680, 513)

staticconstexpr

Coefficient in Butcher array.

Definition at line 88 of file rkf45_formula.h.

◆ a54

template<concepts::problem Problem>

scalar_type num_collect::ode::runge_kutta::rkf45_formula< Problem >::a54 = coeff(-845, 4104)

staticconstexpr

Coefficient in Butcher array.

Definition at line 89 of file rkf45_formula.h.

◆ a61

template<concepts::problem Problem>

scalar_type num_collect::ode::runge_kutta::rkf45_formula< Problem >::a61 = coeff(-8, 27)

staticconstexpr

Coefficient in Butcher array.

Definition at line 90 of file rkf45_formula.h.

◆ a62

template<concepts::problem Problem>

scalar_type num_collect::ode::runge_kutta::rkf45_formula< Problem >::a62 = coeff(2)

staticconstexpr

Coefficient in Butcher array.

Definition at line 91 of file rkf45_formula.h.

◆ a63

template<concepts::problem Problem>

scalar_type num_collect::ode::runge_kutta::rkf45_formula< Problem >::a63 = coeff(-3544, 2565)

staticconstexpr

Coefficient in Butcher array.

Definition at line 92 of file rkf45_formula.h.

◆ a64

template<concepts::problem Problem>

scalar_type num_collect::ode::runge_kutta::rkf45_formula< Problem >::a64 = coeff(1859, 4104)

staticconstexpr

Coefficient in Butcher array.

Definition at line 93 of file rkf45_formula.h.

◆ a65

template<concepts::problem Problem>

scalar_type num_collect::ode::runge_kutta::rkf45_formula< Problem >::a65 = coeff(-11, 40)

staticconstexpr

Coefficient in Butcher array.

Definition at line 94 of file rkf45_formula.h.

◆ b2

template<concepts::problem Problem>

scalar_type num_collect::ode::runge_kutta::rkf45_formula< Problem >::b2 = coeff(1, 4)

staticconstexpr

Coefficient in Butcher array.

Definition at line 96 of file rkf45_formula.h.

◆ b3

template<concepts::problem Problem>

scalar_type num_collect::ode::runge_kutta::rkf45_formula< Problem >::b3 = coeff(3, 8)

staticconstexpr

Coefficient in Butcher array.

Definition at line 97 of file rkf45_formula.h.

◆ b4

template<concepts::problem Problem>

scalar_type num_collect::ode::runge_kutta::rkf45_formula< Problem >::b4 = coeff(12, 13)

staticconstexpr

Coefficient in Butcher array.

Definition at line 98 of file rkf45_formula.h.

◆ b5

template<concepts::problem Problem>

scalar_type num_collect::ode::runge_kutta::rkf45_formula< Problem >::b5 = coeff(1)

staticconstexpr

Coefficient in Butcher array.

Definition at line 99 of file rkf45_formula.h.

◆ b6

template<concepts::problem Problem>

scalar_type num_collect::ode::runge_kutta::rkf45_formula< Problem >::b6 = coeff(1, 2)

staticconstexpr

Coefficient in Butcher array.

Definition at line 100 of file rkf45_formula.h.

◆ c1

template<concepts::problem Problem>

scalar_type num_collect::ode::runge_kutta::rkf45_formula< Problem >::c1 = coeff(16, 135)

staticconstexpr

Coefficient in Butcher array.

Definition at line 102 of file rkf45_formula.h.

◆ c3

template<concepts::problem Problem>

scalar_type num_collect::ode::runge_kutta::rkf45_formula< Problem >::c3 = coeff(6656, 12825)

staticconstexpr

Coefficient in Butcher array.

Definition at line 103 of file rkf45_formula.h.

◆ c4

template<concepts::problem Problem>

scalar_type num_collect::ode::runge_kutta::rkf45_formula< Problem >::c4 = coeff(28561, 56430)

staticconstexpr

Coefficient in Butcher array.

Definition at line 104 of file rkf45_formula.h.

◆ c5

template<concepts::problem Problem>

scalar_type num_collect::ode::runge_kutta::rkf45_formula< Problem >::c5 = coeff(-9, 50)

staticconstexpr

Coefficient in Butcher array.

Definition at line 105 of file rkf45_formula.h.

◆ c6

template<concepts::problem Problem>

scalar_type num_collect::ode::runge_kutta::rkf45_formula< Problem >::c6 = coeff(2, 55)

staticconstexpr

Coefficient in Butcher array.

Definition at line 106 of file rkf45_formula.h.

◆ ce1

template<concepts::problem Problem>

scalar_type num_collect::ode::runge_kutta::rkf45_formula< Problem >::ce1 = c1 - cw1

staticconstexpr

Coefficient in Butcher array.

Definition at line 113 of file rkf45_formula.h.

◆ ce3

template<concepts::problem Problem>

scalar_type num_collect::ode::runge_kutta::rkf45_formula< Problem >::ce3 = c3 - cw3

staticconstexpr

Coefficient in Butcher array.

Definition at line 114 of file rkf45_formula.h.

◆ ce4

template<concepts::problem Problem>

scalar_type num_collect::ode::runge_kutta::rkf45_formula< Problem >::ce4 = c4 - cw4

staticconstexpr

Coefficient in Butcher array.

Definition at line 115 of file rkf45_formula.h.

◆ ce5

template<concepts::problem Problem>

scalar_type num_collect::ode::runge_kutta::rkf45_formula< Problem >::ce5 = c5 - cw5

staticconstexpr

Coefficient in Butcher array.

Definition at line 116 of file rkf45_formula.h.

◆ ce6

template<concepts::problem Problem>

scalar_type num_collect::ode::runge_kutta::rkf45_formula< Problem >::ce6 = c6

staticconstexpr

Coefficient in Butcher array.

Definition at line 117 of file rkf45_formula.h.

◆ cw1

template<concepts::problem Problem>

scalar_type num_collect::ode::runge_kutta::rkf45_formula< Problem >::cw1 = coeff(25, 216)

staticconstexpr

Coefficient in Butcher array.

Definition at line 108 of file rkf45_formula.h.

◆ cw3

template<concepts::problem Problem>

scalar_type num_collect::ode::runge_kutta::rkf45_formula< Problem >::cw3 = coeff(1408, 2565)

staticconstexpr

Coefficient in Butcher array.

Definition at line 109 of file rkf45_formula.h.

◆ cw4

template<concepts::problem Problem>

scalar_type num_collect::ode::runge_kutta::rkf45_formula< Problem >::cw4 = coeff(2197, 4104)

staticconstexpr

Coefficient in Butcher array.

Definition at line 110 of file rkf45_formula.h.

◆ cw5

template<concepts::problem Problem>

scalar_type num_collect::ode::runge_kutta::rkf45_formula< Problem >::cw5 = coeff(-1, 5)

staticconstexpr

Coefficient in Butcher array.

Definition at line 111 of file rkf45_formula.h.

◆ k1_

template<concepts::problem Problem>

variable_type num_collect::ode::runge_kutta::rkf45_formula< Problem >::k1_ {}

private

Intermediate variable.

Definition at line 183 of file rkf45_formula.h.

◆ k2_

template<concepts::problem Problem>

variable_type num_collect::ode::runge_kutta::rkf45_formula< Problem >::k2_ {}

private

Intermediate variable.

Definition at line 184 of file rkf45_formula.h.

◆ k3_

template<concepts::problem Problem>

variable_type num_collect::ode::runge_kutta::rkf45_formula< Problem >::k3_ {}

private

Intermediate variable.

Definition at line 185 of file rkf45_formula.h.

◆ k4_

template<concepts::problem Problem>

variable_type num_collect::ode::runge_kutta::rkf45_formula< Problem >::k4_ {}

private

Intermediate variable.

Definition at line 186 of file rkf45_formula.h.

◆ k5_

template<concepts::problem Problem>

variable_type num_collect::ode::runge_kutta::rkf45_formula< Problem >::k5_ {}

private

Intermediate variable.

Definition at line 187 of file rkf45_formula.h.

◆ k6_

template<concepts::problem Problem>

variable_type num_collect::ode::runge_kutta::rkf45_formula< Problem >::k6_ {}

private

Intermediate variable.

Definition at line 188 of file rkf45_formula.h.

◆ lesser_order

template<concepts::problem Problem>

index_type num_collect::ode::runge_kutta::rkf45_formula< Problem >::lesser_order = 4

staticconstexpr

Order of lesser coefficients of this formula.

Definition at line 67 of file rkf45_formula.h.

◆ log_tag

template<concepts::problem Problem>

auto num_collect::ode::runge_kutta::rkf45_formula< Problem >::log_tag

staticconstexpr

Initial value:

=

logging::log_tag_view("num_collect::ode::runge_kutta::rkf45_formula")

Log tag.

Definition at line 63 of file rkf45_formula.h.

◆ order

template<concepts::problem Problem>

index_type num_collect::ode::runge_kutta::rkf45_formula< Problem >::order = 5

staticconstexpr

Order of this formula.

Definition at line 60 of file rkf45_formula.h.

◆ stages

template<concepts::problem Problem>

index_type num_collect::ode::runge_kutta::rkf45_formula< Problem >::stages = 6

staticconstexpr

Number of stages of this formula.

Definition at line 57 of file rkf45_formula.h.

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

include/num_collect/ode/runge_kutta/rkf45_formula.h

Public Types

Public Member Functions

Static Public Attributes

Private Attributes

Additional Inherited Members

Detailed Description

Member Typedef Documentation

◆ base_type

Member Function Documentation

◆ step()

◆ step_embedded()

Member Data Documentation

◆ a21

◆ a31

◆ a32

◆ a41

◆ a42

◆ a43

◆ a51

◆ a52

◆ a53

◆ a54

◆ a61

◆ a62

◆ a63

◆ a64

◆ a65

◆ b2

◆ b3

◆ b4

◆ b5

◆ b6

◆ c1

◆ c3

◆ c4

◆ c5

◆ c6

◆ ce1

◆ ce3

◆ ce4

◆ ce5

◆ ce6

◆ cw1

◆ cw3

◆ cw4

◆ cw5

◆ k1_

◆ k2_

◆ k3_

◆ k4_

◆ k5_

◆ k6_

◆ lesser_order

◆ log_tag

◆ order

◆ stages