Finite difference method for the fractional order pseudo telegraph integro-differential equation

Abstract

The main goal of this paper is to investigate the numerical solution of the fractional order pseudo telegraph integro-differential equation. We establish the first order finite difference scheme. Then for the stability analysis of the constructed difference scheme, we give theoretical statements and prove them. We also support our theoretical statements by performing numerical experiments for some fractions of order α.

Stability of Finite Difference Schemes to Pseudo-Hyperbolic Telegraph Equation

“…In [9,10], numerical schemes based on H 1 -Galerkin mixed finite element method were constructed for pseudo-hyperbolic equations. Some other works on pseudo-hyperbolic equations are [11]- [15]. There has been a wide range of research on finite difference schemes for approximate solutions to telegraph equations and there are considerable approximation for stability of these difference schemes.…”