Numerical Scheme for Solving the Space-Time Variable Order Nonlinear Fractional Wave Equation

Abstract

In this paper, the space-time variable order fractional wave equation with a nonlinear source term is considered. The derivative is defined in the Caputo sense. The non-standard finite difference method is proposed for solving the variable order fractional wave equation. Special attention is given to study the stability analysis and the truncation error of the method. Some numerical test examples are presented, and the results demonstrate the effectiveness of the method. The obtained results are compared with exact solutions and the standard finite difference solutions.