Numerical Spectral Legendre-Galerkin Algorithm for Solving Time Fractional Telegraph Equation

摘要

This paper is concerned with presenting and analyzing a new technique for solving time fractional telegraph equation. This technique is based on applying the spectral Galerkin method that depends on choosing an appropriate basis functions satisfying the underlying boundary conditions. A double shifted Legendre expansion is proposed as an approximating polynomial. A careful study for the convergence and error analysis of the suggested approximate double expansion is performed. Some numerical results are provided aiming to ensure the efficiency and applicability of the proposed algorithm.