num_collect::ode::symplectic::leap_frog_formula< Problem > Class Template Reference

Class of leap-frog formula. More...

#include <num_collect/ode/symplectic/leap_frog_formula.h>

Inheritance diagram for num_collect::ode::symplectic::leap_frog_formula< Problem >:

Collaboration diagram for num_collect::ode::symplectic::leap_frog_formula< Problem >:

Public Types
using	base_type = formula_base<leap_frog_formula<Problem>, Problem>
	Type of base class.
Public Types inherited from num_collect::ode::formula_base< leap_frog_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.
Public Member Functions inherited from num_collect::ode::formula_base< leap_frog_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 auto	log_tag
	Log tag.
static constexpr index_type	order = 2
	Order of this formula.
static constexpr index_type	stages = 3
	Number of stages of this formula.

Additional Inherited Members
Protected Member Functions inherited from num_collect::ode::formula_base< leap_frog_formula< Problem >, Problem >
auto	derived () const noexcept -> const leap_frog_formula< Problem > &
	Access derived object.
auto	derived () noexcept -> leap_frog_formula< Problem > &
	Access derived object.
Static Protected Member Functions inherited from num_collect::ode::formula_base< leap_frog_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::multi_variate_problem Problem>
class num_collect::ode::symplectic::leap_frog_formula< Problem >

Class of leap-frog formula.

This formula solves initial value problems of ODEs with following structure:

\[ \frac{d}{dt} \begin{pmatrix} \boldsymbol{p} \\ \boldsymbol{q} \end{pmatrix} = \begin{pmatrix} -\frac{\partial V}{\partial \boldsymbol{q}} \\ \frac{\partial T}{\partial \boldsymbol{p}} \end{pmatrix} \]

This formula assumes that the lower half of the solution vector is position \(\boldsymbol{q}\), and the upper half is moment \(\boldsymbol{p}\).

Note

For theoretical discussion, see [5].

Template Parameters

Problem

Type of problem.

Definition at line 60 of file leap_frog_formula.h.

Member Typedef Documentation

base_type

template<concepts::multi_variate_problem Problem>

using num_collect::ode::symplectic::leap_frog_formula< Problem >::base_type = formula_base<leap_frog_formula<Problem>, Problem>

Type of base class.

Definition at line 64 of file leap_frog_formula.h.

Member Function Documentation

step()

template<concepts::multi_variate_problem Problem>

void num_collect::ode::symplectic::leap_frog_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 91 of file leap_frog_formula.h.

Member Data Documentation

log_tag

template<concepts::multi_variate_problem Problem>

auto num_collect::ode::symplectic::leap_frog_formula< Problem >::log_tag

staticconstexpr

Initial value:

= logging::log_tag_view(
        "num_collect::ode::symplectic::leap_frog_formula")

Log tag.

Definition at line 87 of file leap_frog_formula.h.

order

template<concepts::multi_variate_problem Problem>

index_type num_collect::ode::symplectic::leap_frog_formula< Problem >::order = 2

staticconstexpr

Order of this formula.

Definition at line 84 of file leap_frog_formula.h.

stages

template<concepts::multi_variate_problem Problem>

index_type num_collect::ode::symplectic::leap_frog_formula< Problem >::stages = 3

staticconstexpr

Number of stages of this formula.

Definition at line 81 of file leap_frog_formula.h.

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

• include/num_collect/ode/symplectic/leap_frog_formula.h