An Error Analysis of Implicit Finite Difference Method with Mamadu-Njoseh Basis Functions for Time Fractional Telegraph Equation

Abstract

In this paper, we proposed and analyzed the error estimate of an implicit finite difference method with Mamadu-Njoseh as basis functions for time fractional telegraph equation. To enhance the efficacy of the method we first transform the Caputo type fractional derivative into Riemann-Liouville derivatives. The error analysis of the method is stated and proven. Also, the optimal results for scalars unknown in  norm were derived for the two-dimensional case. Numerical illustrations are presented to test the reliability of the analytical and computed results. The resulting numerical evidence shows that the proposed method convergences more rapidly than the standard finite difference method. MAPLE 18 is used for all mathematical procedures in this paper.