brainpy.integrators.ode.explicit_rk.Ralston2
brainpy.integrators.ode.explicit_rk.Ralston2#
- class brainpy.integrators.ode.explicit_rk.Ralston2(f, var_type=None, dt=None, name=None, show_code=False, state_delays=None, neutral_delays=None)[source]#
Ralston’s method for ODEs.
Ralston’s method is a second-order method with two stages and a minimum local error bound.
Given ODEs with a given initial value,
\[y'(t) = f(t,y(t)), \qquad y(t_0)=y_0,\]the Ralston’s second order method is given by
\[y_{n+1}=y_{n}+\frac{h}{4} f\left(t_{n}, y_{n}\right)+ \frac{3 h}{4} f\left(t_{n}+\frac{2 h}{3}, y_{n}+\frac{2 h}{3} f\left(t_{n}, y_{n}\right)\right)\]Therefore, the corresponding Butcher tableau is:
\[\begin{split}\begin{array}{c|cc} 0 & 0 & 0 \\ 2 / 3 & 2 / 3 & 0 \\ \hline & 1 / 4 & 3 / 4 \end{array}\end{split}\]- __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.