A non-polynomial numerical scheme for fourth-order fractional diffusion-wave model

Abstract

In this paper, we tackle the numerical treatment of a fourth-order fractional diffusion-wave problem. By using parametric quintic spline in the spatial dimension and an approximation of Caputo derivatives at half-points, we propose a numerical scheme and rigorously prove its solvability, convergence and stability in maximum norm. It is shown that the theoretical convergence order improves those of earlier work. To confirm, simulation is carried out to demonstrate the numerical efficiency of the proposed scheme as well as the better performance over other methods.