# brainpy.integrators.ode.explicit_rk.ExplicitRKIntegrator#

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

Explicit Runge–Kutta methods for ordinary differential equation.

For the system,

$\frac{d y}{d t}=f(t, y)$

Explicit Runge-Kutta methods take the form

$\begin{split}k_{i}=f\left(t_{n}+c_{i}h,y_{n}+h\sum _{j=1}^{s}a_{ij}k_{j}\right) \\ y_{n+1}=y_{n}+h \sum_{i=1}^{s} b_{i} k_{i}\end{split}$

Each method listed on this page is defined by its Butcher tableau, which puts the coefficients of the method in a table as follows:

$\begin{split}\begin{array}{c|cccc} c_{1} & a_{11} & a_{12} & \ldots & a_{1 s} \\ c_{2} & a_{21} & a_{22} & \ldots & a_{2 s} \\ \vdots & \vdots & \vdots & \ddots & \vdots \\ c_{s} & a_{s 1} & a_{s 2} & \ldots & a_{s s} \\ \hline & b_{1} & b_{2} & \ldots & b_{s} \end{array}\end{split}$
Parameters
• f (callable) – The derivative function.

• show_code (bool) – Whether show the formatted code.

• dt (float) – The numerical precision.

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

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.