brainpy.integrators.sde.SRK1W1

class brainpy.integrators.sde.SRK1W1(f, g, dt=None, name=None, show_code=False, var_type=None, intg_type=None, wiener_type=None)

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

This method has have strong orders :backend:`(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)

Methods

__init__(f, g[, dt, name, show_code, ...])
build()
cpu()
cuda()
ints([method])	Collect all integrators in this node and the children nodes.
load_states(filename[, verbose, check])	Load the model states.
nodes([method, _paths])	Collect all children nodes.
save_states(filename[, all_vars])	Save the model states.
to(devices)
tpu()
train_vars([method])	The shortcut for retrieving all trainable variables.
unique_name([name, type])	Get the unique name for this object.
vars([method])	Collect all variables in this node and the children nodes.

Attributes

implicit_nodes	Used to wrap the implicit children nodes which cannot be accessed by self.xxx
implicit_vars	Used to wrap the implicit variables which cannot be accessed by self.xxx
target_backend	Used to specify the target backend which the model to run.