The Heun–Euler method for ODEs.

The simplest adaptive Runge–Kutta method involves combining Heun’s method, which is order 2, with the Euler method, which is order 1.

It has the characteristics of:

• method stage = 2

• method order = 1

• Butcher Tables:

$\begin{split}\begin{array}{c|cc} 0&\\ 1& 1 \\ \hline & 1/2& 1/2\\ & 1 & 0 \end{array}\end{split}$
__init__(f, var_type=None, dt=None, name=None, adaptive=None, tol=None, show_code=False, state_delays=None, neutral_delays=None)#

Methods

 __init__(f[, var_type, dt, name, adaptive, ...]) 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 B1 B2 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.