A numerical approximation for the solution of a time-fractional telegraph equation based on the Crank–Nicolson method

Abstract

In this paper, a two-dimensional time-fractional telegraph equation is considered with derivative in the sense of Caputo and $ 1<\beta<2$. The aim of this work is to extend the Crank--Nicolson method for this time-fractional telegraph equation. The stability and convergence of the numerical method are investigated. Also, the accuracy and efficiency of the proposed method are demonstrated by numerical experiments.

Keywords

• time-fractional telegraph equation
• crank–nicolson method
• stability
• convergence