brainpy.integrators.ode.AdaptiveRKIntegrator

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

Adaptive Runge-Kutta method for ordinary differential equations.

The embedded methods are designed to produce an estimate of the local truncation error of a single Runge-Kutta step, and as result, allow to control the error with adaptive step-size. This is done by having two methods in the tableau, one with order p and one with order \(p-1\).

The lower-order step is given by

\[y^*_{n+1} = y_n + h\sum_{i=1}^s b^*_i k_i,\]

where the \(k_{i}\) are the same as for the higher order method. Then the error is

\[e_{n+1} = y_{n+1} - y^*_{n+1} = h\sum_{i=1}^s (b_i - b^*_i) k_i,\]

which is \(O(h^{p})\). The Butcher Tableau for this kind of method is extended to give the values of \(b_{i}^{*}\)

\[\begin{split}\begin{array}{c|cccc} c_1 & a_{11} & a_{12}& \dots & a_{1s}\\ c_2 & a_{21} & a_{22}& \dots & a_{2s}\\ \vdots & \vdots & \vdots& \ddots& \vdots\\ c_s & a_{s1} & a_{s2}& \dots & a_{ss} \\ \hline & b_1 & b_2 & \dots & b_s\\ & b_1^* & b_2^* & \dots & b_s^*\\ \end{array}\end{split}\]

Parameters

• f (callable) – The derivative function.

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

• dt (float) – The numerical precision.

• adaptive (bool) – Whether use the adaptive updating.

• tol (float) – The error tolerence.

• var_type (str) – The variable type.

__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()
cpu()	Move all variable into the CPU device.
cuda()	Move all variables into the GPU device.
load_state_dict(state_dict[, warn])	Copy parameters and buffers from state_dict into this module and its descendants.
load_states(filename[, verbose])	Load the model states.
nodes([method, level, include_self])	Collect all children nodes.
register_implicit_nodes(*nodes[, node_cls])
register_implicit_vars(*variables, ...)
save_states(filename[, variables])	Save the model states.
set_integral(f)	Set the integral function.
state_dict()	Returns a dictionary containing a whole state of the module.
to(device)	Moves all variables into the given device.
tpu()	Move all variables into the TPU device.
train_vars([method, level, include_self])	The shortcut for retrieving all trainable variables.
tree_flatten()	Flattens the object as a PyTree.
tree_unflatten(aux, dynamic_values)	New in version 2.3.1.
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.