brainpy.integrators.ode.explicit_rk.Ralston4#

class brainpy.integrators.ode.explicit_rk.Ralston4(f, var_type=None, dt=None, name=None, show_code=False, state_delays=None, neutral_delays=None)[source]#

Ralston’s fourth-order method for ODEs.

It has the characteristics of:

  • method stage = 4

  • method order = 4

  • Butcher Tables:

\[\begin{split}\begin{array}{c|cccc} 0 & 0 & 0 & 0 & 0 \\ .4 & .4 & 0 & 0 & 0 \\ .45573725 & .29697761 & .15875964 & 0 & 0 \\ 1 & .21810040 & -3.05096516 & 3.83286476 & 0 \\ \hline & .17476028 & -.55148066 & 1.20553560 & .17118478 \end{array}\end{split}\]

References

1

Ralston, Anthony (1962). “Runge-Kutta Methods with Minimum Error Bounds”. Math. Comput. 16 (80): 431–437. doi:10.1090/S0025-5718-1962-0150954-0

__init__(f, var_type=None, dt=None, name=None, show_code=False, state_delays=None, neutral_delays=None)#

Methods

__init__(f[, var_type, 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

A

B

C

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.

neutral_delays

neutral delays.

parameters

The parameters defined in the differential equation.

state_delays

State delays.

variables

The variables defined in the differential equation.