# brainpy.integrators.ode.explicit_rk.RK4Rule38#

class brainpy.integrators.ode.explicit_rk.RK4Rule38(f, var_type=None, dt=None, name=None, show_code=False, state_delays=None, neutral_delays=None)[source]#

3/8-rule fourth-order method for ODEs.

A slight variation of “the” Runge–Kutta method is also due to Kutta in 1901 1 and is called the 3/8-rule. The primary advantage this method has is that almost all of the error coefficients are smaller than in the popular method, but it requires slightly more FLOPs (floating-point operations) per time step.

It has the characteristics of:

• method stage = 4

• method order = 4

• Butcher Tables:

$\begin{split}\begin{array}{c|cccc} 0 & 0 & 0 & 0 & 0 \\ 1 / 3 & 1 / 3 & 0 & 0 & 0 \\ 2 / 3 & -1 / 3 & 1 & 0 & 0 \\ 1 & 1 & -1 & 1 & 0 \\ \hline & 1 / 8 & 3 / 8 & 3 / 8 & 1 / 8 \end{array}\end{split}$

References

1

Hairer, Ernst; Nørsett, Syvert Paul; Wanner, Gerhard (1993), Solving ordinary differential equations I: Nonstiff problems, Berlin, New York: Springer-Verlag, ISBN 978-3-540-56670-0.

__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.