Time discretization

class struphy.ode.solvers.ODEsolverFEEC(vector_field: dict, butcher: ButcherTableau = ButcherTableau(algo='rk4'))

Bases: object

Solver for FEEC coefficients based on explicit s-stage Runge-Kutta methods.

Parameters:

• vector_field (dict) – The vector field of the ODE as a dictionary. Keys are the variables to be updated (i.e. Stencil- or BlockVectors), values are callables representing the respective component of the vector field. That means dy_i/dt = f_i(y_1, …, y_n) for i = 1,…,n, where n is the number of variables.

• algo (str) – See ButcherTableau for available algorithms.

property vector_field

The vector field of the ode as a dictionary. Keys are the variables to be updated (i.e. Stencil- or BlockVectors), values are callables representing the respective component of the vector field.

property y

List of variables to be updated.

property yn

List of allocated space for initial conditions for each variable.

property butcher

See ButcherTableau.

property k

Dictionary of k values for each stage; keys are the variables and values are lists with one allocated k-vector for each stage.

class struphy.ode.utils.ButcherTableau(algo: Literal['rk4', 'forward_euler', 'heun2', 'rk2', 'heun3', '3/8 rule'] = 'rk4')

Bases: object

Butcher tableau for explicit s-stage Runge-Kutta methods.

The Butcher tableau has the form

Parameters:

algo (OptsButcher) – Name of the RK method.

algo: Literal['rk4', 'forward_euler', 'heun2', 'rk2', 'heun3', '3/8 rule'] = 'rk4'

__available_methods__ = ('rk4', 'forward_euler', 'heun2', 'rk2', 'heun3', '3/8 rule')

property a

Characteristic coefficients of the method (see tableau in class docstring).

property b

Characteristic coefficients of the method (see tableau in class docstring).

property c

Characteristic coefficients of the method (see tableau in class docstring).

property n_stages

Number of stages of the s-stage Runge-Kutta method.

property conv_rate

Convergence rate of the s-stage Runge-Kutta method.