brainpy.integrators.sde.srk_scalar.SRK1W1#

class brainpy.integrators.sde.srk_scalar.SRK1W1(f, g, dt=None, name=None, show_code=False, var_type=None, intg_type=None, wiener_type=None, state_delays=None)[source]#

Order 2.0 weak SRK methods for SDEs with scalar Wiener process.

This method has have strong orders \((p_d, p_s) = (2.0,1.5)\).

The Butcher table is:

\[\begin{split}\begin{array}{l|llll|llll|llll} 0 &&&&& &&&& &&&& \\ 3/4 &3/4&&&& 3/2&&& &&&& \\ 0 &0&0&0&& 0&0&0&& &&&&\\ \hline 0 \\ 1/4 & 1/4&&& & 1/2&&&\\ 1 & 1&0&&& -1&0&\\ 1/4& 0&0&1/4&& -5&3&1/2\\ \hline & 1/3& 2/3& 0 & 0 & -1 & 4/3 & 2/3&0 & -1 &4/3 &-1/3 &0 \\ \hline & &&&& 2 &-4/3 & -2/3 & 0 & -2 & 5/3 & -2/3 & 1 \end{array}\end{split}\]

References

1

Rößler, Andreas. “Strong and weak approximation methods for stochastic differential equations—some recent developments.” Recent developments in applied probability and statistics. Physica-Verlag HD, 2010. 127-153.

2

Rößler, Andreas. “Runge–Kutta methods for the strong approximation of solutions of stochastic differential equations.” SIAM Journal on Numerical Analysis 48.3 (2010): 922-952.

__init__(f, g, dt=None, name=None, show_code=False, var_type=None, intg_type=None, wiener_type=None, state_delays=None)[source]#

Methods

__init__(f, g[, dt, name, show_code, ...])

build()

load_states(filename[, verbose])

Load the model states.

nodes([method, level, include_self])

Collect all children nodes.

register_implicit_nodes(*nodes, **named_nodes)

register_implicit_vars(*variables, ...)

save_states(filename[, variables])

Save the model states.

set_integral(f)

Set the integral function.

train_vars([method, level, include_self])

The shortcut for retrieving all trainable variables.

unique_name([name, type_])

Get the unique name for this object.

vars([method, level, include_self])

Collect all variables in this node and the children nodes.

Attributes

arguments

All arguments when calling the numer integrator of the differential equation.

dt

The numerical integration precision.

integral

The integral function.

name

Name of the model.

parameters

The parameters defined in the differential equation.

state_delays

State delays.

variables

The variables defined in the differential equation.