Numerical solution for Fokker-Planck equation using a two-level scheme

TL;DR

This paper introduces a two-level numerical scheme for solving the Fokker-Planck equation that improves computational efficiency while maintaining second-order accuracy and probability conservation.

Contribution

It presents a novel two-level scheme with a factor-three-coarsening strategy that significantly reduces computational cost for Fokker-Planck equations.

Findings

Significant reduction in CPU time achieved.

Maintains second-order accuracy.

Ensures positivity and probability conservation.

Abstract

A numerical solution to the Fokker-Planck equation using a two-level scheme is presented. The Fokker-Planck (FP) equation is of parabolic type equation govern the time evolution of probability density function of the stochastic processes. The FP equation also preserves the positivity and conservative of the total probability. A Chang-Cooper discretization scheme is used to ensure the positiveness and conservation of the total probability with second-order accuracy. We investigate a two-level scheme with factor-three-coarsening strategy and have a significant reduction in computations and CPU time. Numerical experiments are performed to validate the efficiency and second-order accuracy of the proposed two-level algorithm with backward time-difference schemes.