A numerical scheme with high accuracy to solve the two-dimensional time-space diffusion wave model in terms of the Riemann-Liouville and Riesz fractional derivatives

In this paper, we propose a hybrid and efficient numerical scheme with high accuracy to obtain approximate solutions of the two-dimensional time-space diffusion-wave model in terms of the Riemann-Liouville and Riesz fractional derivatives. To discretize the presented model, two approaches are used in the spatial and temporal directions. In the time direction, we use a second-order accurate difference numerical method and the weighted shifted Grünwald derivative approximation of second order. The weighted shifted Grünwald derivative approximation is used to estimate the Riemann–Liouville fractional operator. Also, in the space direction, the Galerkin spectral method based on the modified Jacobi functions is used. The study of convergence and stability analyses for the proposed numerical approach is presented. At the end, some numerical examples are given to show the effectiveness of the proposed numerical scheme. For all the examples, graphs are drawn, and numerical results are reported in tables.

کلیدواژه ها:

Diffusion-wave model ، Weakly singular kernel ، Riesz fractional operator ، Galerkin spectral method ، stability and convergence