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)[source]#

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, **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.