High-order compact finite volume scheme for the 2D multi-term time fractional sub-diffusion equation

Baojin Su,Ziwen Jiang

doi:10.1186/s13662-020-03128-4

Abstract

Based on an L1 interpolation operator, a new high-order compact finite volume scheme is derived for the 2D multi-term time fractional sub-diffusion equation. It is shown that the difference scheme is unconditionally convergent and stable in L_{infty }-norm. The convergence order is O(tau ^{2-alpha }+h_{1}^{4}+h_{2}^{4}), where τ is the temporal step size and h_{1} is the spatial step size in one direction, h_{2} is the spatial step size in another direction. Two numerical examples are implemented, testifying to their efficiency and confirming their convergence order.

Highlights

The study of fractional partial differential equations has attracted many scholars’ attention in recent decades [27,28,29, 32]
Some physical phenomena cannot be described by single-term time fractional partial differential equations, and they have to be described by multi-term time fractional partial differential equations [4]
Because the fractional integrals and derivatives satisfy the nonlocal properties, fractional-order partial differential equations are different from classical partial differential equations

Summary

Introduction

The study of fractional partial differential equations has attracted many scholars’ attention in recent decades [27,28,29, 32]. Chen and Liu structured a finite difference method for two-dimensional anomalous sub-diffusion equation, and they analyzed the stability and convergence of the scheme [7]. Yuste and Acedo found a finite difference method which can solve the time fractional diffusion equation by using a forward Euler scheme, and they discussed the stability and convergence of the scheme [48].

Results

Conclusion