brainpy.integrators.ode.explicit_rk.Ralston3

class brainpy.integrators.ode.explicit_rk.Ralston3(f, var_type=None, dt=None, name=None, show_code=False, state_delays=None, neutral_delays=None)

Ralston’s third-order method for ODEs.

It has the characteristics of:

• method stage = 3

• method order = 3

• Butcher Tables:

\[\begin{split}\begin{array}{c|ccc} 0 & 0 & 0 & 0 \\ 1 / 2 & 1 / 2 & 0 & 0 \\ 3 / 4 & 0 & 3 / 4 & 0 \\ \hline & 2 / 9 & 1 / 3 & 4 / 9 \end{array}\end{split}\]

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)
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
arg_names
arguments	All arguments when calling the numer integrator of the differential equation.
dt	The numerical integration precision.
integral	The integral function.
name
neutral_delays	neutral delays.
parameters	The parameters defined in the differential equation.
state_delays	State delays.
variables	The variables defined in the differential equation.