On the stability analysis of weighted average finite difference methods for fractional wave equation

Abstract

In this article, a numerical study for the fractional wave equations is introduced by using a class of finite difference methods. These methods are extension of the weighted aver- age methods for ordinary (non-fractional) wave equations. The stability analysis of the proposed methods is given by a recently proposed procedure similar to the standard John von Neumann sta- bility analysis. Simple and accurate stability criterion valid for different discretization schemes of the fractional derivative, arbitrary weight factor, and arbitrary order of the fractional deriva- tive, is given and checked numerically. Numerical test example and comparisons have been presented for clarity.