brainpy.integrators.ode.RKF45#

class brainpy.integrators.ode.RKF45(f, var_type=None, dt=None, name=None, adaptive=None, tol=None, show_code=False, state_delays=None, neutral_delays=None)[source]#

The Runge–Kutta–Fehlberg method for ODEs.

The method presented in Fehlberg’s 1969 paper has been dubbed the RKF45 method, and is a method of order $$O(h^4)$$ with an error estimator of order $$O(h^5)$$. The novelty of Fehlberg’s method is that it is an embedded method from the Runge–Kutta family, meaning that identical function evaluations are used in conjunction with each other to create methods of varying order and similar error constants.

Its Butcher table is:

$\begin{split}\begin{array}{l|lllll} 0 & & & & & & \\ 1 / 4 & 1 / 4 & & & & \\ 3 / 8 & 3 / 32 & 9 / 32 & & \\ 12 / 13 & 1932 / 2197 & -7200 / 2197 & 7296 / 2197 & \\ 1 & 439 / 216 & -8 & 3680 / 513 & -845 / 4104 & & \\ 1 / 2 & -8 / 27 & 2 & -3544 / 2565 & 1859 / 4104 & -11 / 40 & \\ \hline & 16 / 135 & 0 & 6656 / 12825 & 28561 / 56430 & -9 / 50 & 2 / 55 \\ & 25 / 216 & 0 & 1408 / 2565 & 2197 / 4104 & -1 / 5 & 0 \end{array}\end{split}$

References

__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, compatible]) 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[, var_cls]) 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) Unflatten the data to construct an object of this class. 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.