An efficient numerical treatment of fourth-order fractional diffusion-wave problems

In this paper, we consider the numerical treatment of a fourth-order fractional diffusion-wave problem. Our proposed method includes the use of parametric quintic spline in the spatial dimension and the weighted shifted Grunwald-Letnikov approximation of fractional integral. The solvability, stability, and convergence of the numerical scheme are rigorously proved. It is shown that the theoretical convergence order improves those of earlier work. Simulation is further carried out to demonstrate the numerical efficiency of the proposed scheme and to compare with other methods.