brainpy.integrators.sde.srk_scalar.SRK2W1
brainpy.integrators.sde.srk_scalar.SRK2W1#
- class brainpy.integrators.sde.srk_scalar.SRK2W1(f, g, dt=None, name=None, show_code=False, var_type=None, intg_type=None, wiener_type=None, state_delays=None)[source]#
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)[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)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
arg_names
arguments
All arguments when calling the numer integrator of the differential equation.
dt
The numerical integration precision.
integral
The integral function.
name
parameters
The parameters defined in the differential equation.
state_delays
State delays.
variables
The variables defined in the differential equation.