brainpy.integrators.ode.explicit_rk.ExplicitRKIntegrator
brainpy.integrators.ode.explicit_rk.ExplicitRKIntegrator#
- class brainpy.integrators.ode.explicit_rk.ExplicitRKIntegrator(f, var_type=None, dt=None, name=None, show_code=False, state_delays=None, neutral_delays=None)[source]#
Explicit Runge–Kutta methods for ordinary differential equation.
For the system,
\[\frac{d y}{d t}=f(t, y)\]Explicit Runge-Kutta methods take the form
\[\begin{split}k_{i}=f\left(t_{n}+c_{i}h,y_{n}+h\sum _{j=1}^{s}a_{ij}k_{j}\right) \\ y_{n+1}=y_{n}+h \sum_{i=1}^{s} b_{i} k_{i}\end{split}\]Each method listed on this page is defined by its Butcher tableau, which puts the coefficients of the method in a table as follows:
\[\begin{split}\begin{array}{c|cccc} c_{1} & a_{11} & a_{12} & \ldots & a_{1 s} \\ c_{2} & a_{21} & a_{22} & \ldots & a_{2 s} \\ \vdots & \vdots & \vdots & \ddots & \vdots \\ c_{s} & a_{s 1} & a_{s 2} & \ldots & a_{s s} \\ \hline & b_{1} & b_{2} & \ldots & b_{s} \end{array}\end{split}\]- Parameters
- __init__(f, var_type=None, dt=None, name=None, show_code=False, state_delays=None, neutral_delays=None)[source]#
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.