Finite Difference and Sinc-Collocation Approximations to a Class of Fractional Diffusion-Wave Equations

Abstract

We propose an efficient numerical method for a class of fractional diffusion-wave equations with the Caputo fractional derivative of order $\alpha$. This approach is based on the finite difference in time and the global sinc collocation in space. By utilizing the collocation technique and some properties of the sinc functions, the problem is reduced to the solution of a system of linear algebraic equations at each time step. Stability and convergence of the proposed method are rigorously analyzed. The numerical solution is of $3-\alpha$ order accuracy in time and exponential rate of convergence in space. Numerical experiments demonstrate the validity of the obtained method and support the obtained theoretical results.