brainpy.integrators.ode.adaptive_rk.RKF12

class brainpy.integrators.ode.adaptive_rk.RKF12(f, var_type=None, dt=None, name=None, adaptive=None, tol=None, show_code=False, state_delays=None, neutral_delays=None)

The Fehlberg RK1(2) method for ODEs.

The Fehlberg method has two methods of orders 1 and 2.

It has the characteristics of:

• method stage = 2

• method order = 1

• Butcher Tables:

\[\begin{split}\begin{array}{l|ll} 0 & & \\ 1 / 2 & 1 / 2 & \\ 1 & 1 / 256 & 255 / 256 & \\ \hline & 1 / 512 & 255 / 256 & 1 / 512 \\ & 1 / 256 & 255 / 256 & 0 \end{array}\end{split}\]

References

1

Fehlberg, E. (1969-07-01). “Low-order classical Runge-Kutta formulas with stepsize control and their application to some heat transfer problems”

__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)
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
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.