A Monotone Finite Volume Method for Time Fractional Fokker-Planck Equations

TL;DR

This paper introduces a monotone finite volume method for time fractional Fokker-Planck equations, ensuring stability, nonnegativity, and improved convergence rates with finer spatial grids, supported by numerical validation.

Contribution

It presents a novel monotone finite volume scheme with proven stability and convergence properties for time fractional Fokker-Planck equations, including enhanced accuracy with finer grids.

Findings

Unconditionally stable numerical scheme.

Order 1 convergence in space, improved to order 2 with finer grids.

Numerical results confirm theoretical stability and convergence.

Abstract

We develop a monotone finite volume method for the time fractional Fokker-Planck equations and theoretically prove its unconditional stability. We show that the convergence rate of this method is order 1 in space and if the space grid becomes sufficiently fine, the convergence rate can be improved to order 2. Numerical results are given to support our theoretical findings. One characteristic of our method is that it has monotone property such that it keeps the nonnegativity of some physical variables such as density, concentration, etc.