Numerical solution of fractional telegraph differential equations by theta-method

Abstract

Difference schemes for theta method are constructed. Theta method is used to deal with fractional telegraph differential equation defined by Caputo fractional derivative for different values of theta = 0.1, 0.5, 0.9 and fractional orders alpha = 0.05, 0.1, 0.5, 0.9, 0.95. The stability of difference schemes for this problem is proved by matrix method and the stability of the exact solution is also given. Numerical results with respect to the exact solution confirm the accuracy and effectiveness of the proposed method.