Numerical Solvers for SDEs

BrainPy provides several numerical methods for stochastic differential equations (SDEs). Specifically, we provide explicit Runge-Kutta methods, derivative-free Milstein methods, and exponential Euler method for SDE numerical integration. For the introductionary tutorial for how to use BrainPy provided numerical solversfor SDEs, please see the document in Quickstart/Numerical Solvers.

[1]:
import brainpy as bp

bp.__version__
[1]:
'1.1.0-alpha'
[2]:
import matplotlib.pyplot as plt

%matplotlib inline

Supported methods for SDEs

BrainPy provides several numerical methods for stochastic differential equations (SDEs). Specifically, we provide explicit Runge-Kutta methods, derivative-free Milstein methods, and exponential Euler method for SDE numerical integration.

Methods

Keywords

Ito SDE support

Stratonovich SDE support

Scalar Wiener support

Vector Wiener support

Strong SRK scheme: SRI1W1

srk1w1_scalar

Yes

Yes

Strong SRK scheme: SRI2W1

srk2w1_scalar

Yes

Yes

Strong SRK scheme: KlPl

KlPl_scalar

Yes

Yes

Euler method

euler

Yes

Yes

Yes

Yes

Heun method

heun

Yes

Yes

Yes

Derivative-free Milstein

milstein

Yes

Yes

Yes

Yes

Exponential Euler

exponential_euler

Yes

Yes

Yes