Gauss-Lobatto-Legendre-Birkhoff pseudospectral approximations for the multi-term time fractional diffusion-wave equation with Neumann boundary conditions

摘要

A second-order finite difference/pseudospectral scheme is proposed for numerical approximation of multi-term time fractional diffusion-wave equation with Neumann boundary conditions. The scheme is based upon the weighted and shifted Grunwald difference operators approximation of the time fractional calculus and Gauss-Lobatto-Legendre-Birkhoff (GLLB) pseudospectral method for spatial discretization. The unconditionally stability and convergence of the scheme are rigorously proved. Numerical examples are carried out to verify theoretical results.