brainpy.integrators.ode.explicit_rk.Ralston2#

class brainpy.integrators.ode.explicit_rk.Ralston2(f, var_type=None, dt=None, name=None, show_code=False, state_delays=None, neutral_delays=None)[source]#

Ralston’s method for ODEs.

Ralston’s method is a second-order method with two stages and a minimum local error bound.

Given ODEs with a given initial value,

$y'(t) = f(t,y(t)), \qquad y(t_0)=y_0,$

the Ralston’s second order method is given by

$y_{n+1}=y_{n}+\frac{h}{4} f\left(t_{n}, y_{n}\right)+ \frac{3 h}{4} f\left(t_{n}+\frac{2 h}{3}, y_{n}+\frac{2 h}{3} f\left(t_{n}, y_{n}\right)\right)$

Therefore, the corresponding Butcher tableau is:

$\begin{split}\begin{array}{c|cc} 0 & 0 & 0 \\ 2 / 3 & 2 / 3 & 0 \\ \hline & 1 / 4 & 3 / 4 \end{array}\end{split}$
__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.