brainpy.integrators module

ODE integrators

Base ODE Integrator

ODEIntegrator(f[, var_type, dt, name, ...])

Numerical Integrator for Ordinary Differential Equations (ODEs).

Generic ODE Functions

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

Explicit Runge-Kutta ODE Integrators

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

Adaptive Runge-Kutta ODE Integrators

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

Exponential ODE Integrators

ExponentialEuler(f[, var_type, dt, name, ...])

Exponential Euler method using automatic differentiation.

SDE integrators

Base SDE Integrator

SDEIntegrator(f, g[, dt, name, show_code, ...])

SDE Integrator.

Generic SDE Functions

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

Normal SDE Integrators

Euler(f, g[, dt, name, show_code, var_type, ...])	Euler method for the Ito and Stratonovich integrals.
Heun(f, g[, dt, name, show_code, var_type, ...])	The Euler-Heun method for Stratonovich integral scheme.
Milstein(f, g[, dt, name, show_code, ...])	Milstein method for Ito or Stratonovich integrals.
MilsteinGradFree(f, g[, dt, name, ...])	Derivative-free Milstein method for Ito or Stratonovich integrals.
ExponentialEuler(f, g[, dt, name, ...])	First order, explicit exponential Euler method.

SRK methods for scalar Wiener process

SRK1W1(f, g[, dt, name, show_code, ...])	Order 2.0 weak SRK methods for SDEs with scalar Wiener process.
SRK2W1(f, g[, dt, name, show_code, ...])	Order 1.5 Strong SRK Methods for SDEs with Scalar Noise.
KlPl(f, g[, dt, name, show_code, var_type, ...])

FDE integrators

Base FDE Integrator

FDEIntegrator(f, alpha, num_memory[, dt, ...])

Numerical integrator for fractional differential equations (FEDs).

Generic FDE Functions

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

Methods for Caputo Fractional Derivative

CaputoEuler(f, alpha, num_memory, inits[, ...])	One-step Euler method for Caputo fractional differential equations.
CaputoL1Schema(f, alpha, num_memory, inits)	The L1 scheme method for the numerical approximation of the Caputo fractional-order derivative equations [3]_.

Methods for Riemann-Liouville Fractional Derivative

GLShortMemory(f, alpha, inits, num_memory[, ...])

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