Numerical solution of fractional telegraph equation via the Tau method

Abstract

This paper presents a computational technique based on the Tau method and Legendre polynomials for the solution of a class of time-fractional telegraph equations. An appropriate representation of the solution via the Legendre oper- ational matrix of fractional derivative is used to reduces its numerical treatment to the solution of a set of linear algebraic equations. The fractional derivatives are described based on the Caputo sense. The method is easy to implement and yields very accurate results. Illustrative examples are included to demonstrate the validity and applicability of the proposed technique.