Namespace of symplectic integration. More...

Classes
class	leap_frog_formula
	Class of leap-frog formula. More...

class	symplectic_forest4_formula
	Class of fourth-order symplectic integration formula in [5]. More...

Typedefs
template<concepts::problem Problem>
using	leap_frog_solver = simple_solver<leap_frog_formula<Problem>>
	Class of solver using leap-frog formula.

template<concepts::problem Problem>
using	symplectic_forest4_solver
	Class of fourth-order symplectic integration formula in [5].

Detailed Description

Namespace of symplectic integration.

Typedef Documentation

◆ leap_frog_solver

template<concepts::problem Problem>

using num_collect::ode::symplectic::leap_frog_solver = simple_solver<leap_frog_formula<Problem>>

Class of solver using 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 140 of file leap_frog_formula.h.

◆ symplectic_forest4_solver

template<concepts::problem Problem>

using num_collect::ode::symplectic::symplectic_forest4_solver

Initial value:

simple_solver<symplectic_forest4_formula<Problem>>

Class of fourth-order symplectic integration formula in [5].