Recently, variable-order nonlocal models have gained a lot of attention in the study of heterogeneous media. However, their numerical studies still remain scant, and the main challenges are from their nonlocality and heterogeneity. In this talk, I will present a Fourier pseudospectral method for solving the variable-order fractional wave equation. For constant-order wave equations, the fast Fourier transforms can be used for their efficient implementation. In contrast to it, the spatial heterogeneity of the variable-order wave equations makes the fast Fourier transform fail, which leads to huge computational and storage costs, especially in high dimensions. To deal with this, a fast algorithm is proposed. The accuracy and efficiency of our method will be studied. Our method can achieve a spectral order of accuracy in space and a second-order of accuracy in time.
Thackeray Hall 427