brainpy.integrators module

ODE integrators

Base ODE Integrator

ODEIntegrator

Numerical Integrator for Ordinary Differential Equations (ODEs).

Generic ODE Functions

set_default_odeint	Set the default ODE numerical integrator method for differential equations.
get_default_odeint	Get the default ODE numerical integrator method.
register_ode_integrator	Register a new ODE integrator.
get_supported_methods	Get all supported numerical methods for DDEs.

Explicit Runge-Kutta ODE Integrators

ExplicitRKIntegrator	Explicit Runge–Kutta methods for ordinary differential equation.
Euler	The Euler method for ODEs.
MidPoint	Explicit midpoint method for ODEs.
Heun2	Heun's method for ODEs.
Ralston2	Ralston's method for ODEs.
RK2	Generic second order Runge-Kutta method for ODEs.
RK3	Classical third-order Runge-Kutta method for ODEs.
Heun3	Heun's third-order method for ODEs.
Ralston3	Ralston's third-order method for ODEs.
SSPRK3	Third-order Strong Stability Preserving Runge-Kutta (SSPRK3).
RK4	Classical fourth-order Runge-Kutta method for ODEs.
Ralston4	Ralston's fourth-order method for ODEs.
RK4Rule38	3/8-rule fourth-order method for ODEs.

Adaptive Runge-Kutta ODE Integrators

AdaptiveRKIntegrator	Adaptive Runge-Kutta method for ordinary differential equations.
RKF12	The Fehlberg RK1(2) method for ODEs.
RKF45	The Runge–Kutta–Fehlberg method for ODEs.
DormandPrince	The Dormand–Prince method for ODEs.
CashKarp	The Cash–Karp method for ODEs.
BogackiShampine	The Bogacki–Shampine method for ODEs.
HeunEuler	The Heun–Euler method for ODEs.

Exponential ODE Integrators

ExponentialEuler

Exponential Euler method using automatic differentiation.

SDE integrators

Base SDE Integrator

SDEIntegrator

SDE Integrator.

Generic SDE Functions

set_default_sdeint	Set the default SDE numerical integrator method for differential equations.
get_default_sdeint	Get the default SDE numerical integrator method.
register_sde_integrator	Register a new SDE integrator.
get_supported_methods	Get all supported numerical methods for DDEs.

Normal SDE Integrators

Euler	Euler method for the Ito and Stratonovich integrals.
Heun	The Euler-Heun method for Stratonovich integral scheme.
Milstein	Milstein method for Ito or Stratonovich integrals.
MilsteinGradFree	Derivative-free Milstein method for Ito or Stratonovich integrals.
ExponentialEuler	First order, explicit exponential Euler method.

SRK methods for scalar Wiener process

SRK1W1	Order 2.0 weak SRK methods for SDEs with scalar Wiener process.
SRK2W1	Order 1.5 Strong SRK Methods for SDEs with Scalar Noise.
KlPl

FDE integrators

Base FDE Integrator

FDEIntegrator

Numerical integrator for fractional differential equations (FEDs).

Generic FDE Functions

set_default_fdeint	Set the default ODE numerical integrator method for differential equations.
get_default_fdeint	Get the default ODE numerical integrator method.
register_fde_integrator	Register a new ODE integrator.
get_supported_methods	Get all supported numerical methods for DDEs.

Methods for Caputo Fractional Derivative

CaputoEuler	One-step Euler method for Caputo fractional differential equations.
CaputoL1Schema	The L1 scheme method for the numerical approximation of the Caputo fractional-order derivative equations [3]_.

Methods for Riemann-Liouville Fractional Derivative

GLShortMemory

Efficient Computation of the Short-Memory Principle in Grünwald-Letnikov Method [1]_.