Numerical solution of fractional Riesz space telegraph equation

Document Type : Research Paper


1 Faculty of Mathematical Sciences, University of Tabriz, Tabriz, Iran.

2 Departement of Mathematics, Islamic Azad University Tabriz Branch, Tabriz, Iran.


In this paper, a numerical method based on polynomial approximation is presented for the Riesz fractional telegraph equation. First, a system of fractional differential equations are obtained from the telegraph equation with respect to the time variable by using the method of lines. Then a new numerical algorithm, as well as its modification for solving fractional differential equations (FDEs) based on the polynomial interpolation, is proposed. The algorithms are designed to estimate to linear fractional systems. The convergence order and stability of the fractional order algorithms are proved. At the end three examples with known exact solutions are chosen. Numerical results show that accuracy of present scheme is of order O(∆t 2 ).