Fokker-Planck Solution

A MATLAB mex implementation for numerically solving the Fokker-Planck equation using the Chang-Cooper method.

Description

This package provides a C-based MEX function (FP4) for solving the Fokker-Planck equation, which describes the temporal evolution of probability densities in diffusion processes.

Files

• FP4.c - Source code for the MEX function
• FP4.mex* - Compiled MEX binaries for different platforms (Windows, Mac, Linux)
• tutorial_FokkerPlanck.m - Example script demonstrating usage and comparing different numerical methods

Usage

[ufinal, Pt, Pt_bound, Pg0, Pxt] = FP4(xmesh, uinit, k, sigma, bound_change, bound_margin, dt)

Input Parameters

• xmesh - Spatial grid (column vector)
• uinit - Initial probability density (column vector)
• k - Drift rate
• sigma - Standard deviation of the diffusion process
• bound_change - Matrix with two columns specifying how boundaries change over time
• bound_margin - Vector [lb_margin; ub_margin] specifying boundary margins
• dt - Time step size

Output Parameters

• ufinal - Final probability density
• Pt - Survivor function (probability of not crossing bounds)
• Pt_bound - Probability of crossing lower and upper bounds at each time step
• Pg0 - Probability of being above zero at each time step
• Pxt - Full probability density across space and time (optional, memory-intensive)

Example

See tutorial_FokkerPlanck.m for an example comparing different numerical methods.

Credit

Kiani lab (roozbeh@nyu.edu)

http://www.cns.nyu.edu/kianilab/Home.html

The code is released under a BSD license.