brainpy.integrators.sde.SRK2W1

class brainpy.integrators.sde.SRK2W1(f, g, dt=None, name=None, show_code=False, var_type=None, intg_type=None, wiener_type=None, state_delays=None)

Order 1.5 Strong SRK Methods for SDEs with Scalar Noise.

This method has have strong orders \((p_d, p_s) = (3.0,1.5)\).

The Butcher table is:

\[\begin{split}\begin{array}{c|cccc|cccc|ccc|} 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & & & & \\ 1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & & & & \\ 1 / 2 & 1 / 4 & 1 / 4 & 0 & 0 & 1 & 1 / 2 & 0 & 0 & & & & \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & & & & \\ \hline 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & & & & \\ 1 / 4 & 1 / 4 & 0 & 0 & 0 & -1 / 2 & 0 & 0 & 0 & & & & \\ 1 & 1 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & & & & \\ 1 / 4 & 0 & 0 & 1 / 4 & 0 & 2 & -1 & 1 / 2 & 0 & & & & \\ \hline & 1 / 6 & 1 / 6 & 2 / 3 & 0 & -1 & 4 / 3 & 2 / 3 & 0 & -1 & -4 / 3 & 1 / 3 & 0 \\ \hline & & & & &2 & -4 / 3 & -2 / 3 & 0 & -2 & 5 / 3 & -2 / 3 & 1 \end{array}\end{split}\]

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)

Methods

__init__(f, g[, dt, name, show_code, ...])
build()
cpu()	Move all variable into the CPU device.
cuda()	Move all variables into the GPU device.
load_state_dict(state_dict[, warn])	Copy parameters and buffers from state_dict into this module and its descendants.
load_states(filename[, verbose])	Load the model states.
nodes([method, level, include_self])	Collect all children nodes.
register_implicit_nodes(*nodes[, node_cls])
register_implicit_vars(*variables, ...)
save_states(filename[, variables])	Save the model states.
set_integral(f)	Set the integral function.
state_dict()	Returns a dictionary containing a whole state of the module.
to(device)	Moves all variables into the given device.
tpu()	Move all variables into the TPU device.
train_vars([method, level, include_self])	The shortcut for retrieving all trainable variables.
tree_flatten()	Flattens the object as a PyTree.
tree_unflatten(aux, dynamic_values)	New in version 2.3.1.
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.