A weighted numerical algorithm for two and three dimensional two-sided space fractional wave equations

摘要

A weighed numerical scheme that can effectively solve the fractional wave equation in a finite domain is provided. We focus on detailedly discussing the two and three dimensional two-sided space fractional wave equations with homogeneous boundary conditions. A second order finite difference scheme is used to discretize the space fractional derivative and the time derivative. Additionally, the numerical results confirm that the weighted numerical algorithm is convergent with second order accuracy in both space and time directions for the homogeneous boundary fractional problems.