brainpy.integrators.ode.explicit_rk.Ralston4
brainpy.integrators.ode.explicit_rk.Ralston4#
- class brainpy.integrators.ode.explicit_rk.Ralston4(f, var_type=None, dt=None, name=None, show_code=False, state_delays=None, neutral_delays=None)[source]#
Ralston’s fourth-order method for ODEs.
It has the characteristics of:
method stage = 4
method order = 4
Butcher Tables:
\[\begin{split}\begin{array}{c|cccc} 0 & 0 & 0 & 0 & 0 \\ .4 & .4 & 0 & 0 & 0 \\ .45573725 & .29697761 & .15875964 & 0 & 0 \\ 1 & .21810040 & -3.05096516 & 3.83286476 & 0 \\ \hline & .17476028 & -.55148066 & 1.20553560 & .17118478 \end{array}\end{split}\]References
- 1
Ralston, Anthony (1962). “Runge-Kutta Methods with Minimum Error Bounds”. Math. Comput. 16 (80): 431–437. doi:10.1090/S0025-5718-1962-0150954-0
- __init__(f, var_type=None, dt=None, name=None, show_code=False, state_delays=None, neutral_delays=None)#
Methods
__init__
(f[, var_type, dt, name, show_code, ...])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
B
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.