Approximation of the Fractional Variable Order Wave Model by Weighted Average Finite Difference Method

Abstract

In this article we examine the weighted average finite difference methods to approximate the fractional variable-order wave equation, where, the order of the differentiation can be a function of time. The fractional differentiation of the of variable-order are described in terms of the Riemann-Liouville concept. The stability of the utilized method are proved by using a kind of Von Neumann analysis. To reveals that the method is effective, two examples are offered. and the obtained solutions were compared with the exact solutions.