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)[source]#

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, **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.