A fast difference scheme for the variable coefficient time-fractional diffusion wave equations

Abstract In this paper, we focus on the fast computation for solving the fourth-order time fractional diffusion wave equations with variable coefficient. A fast difference scheme is derived by applying the FL 2 − 1 σ formula to approximate the time Caputo fractional derivative. The resulting FL 2 − 1 σ scheme keeps the almost same accuracy with the traditional L 2 − 1 σ scheme, but it reduces the computational complexity significantly. The solvability, unconditional stability and convergence under the maximum norm of the scheme are proved strictly by using the discrete energy method. Numerical results are given to verify the performance of our scheme.