A fast temporal second-order compact ADI difference scheme for the 2D multi-term fractional wave equation

Abstract

In this paper, a fast temporal second-order compact ADI scheme is proposed for the 2D time multi-term fractional wave equation. At the super-convergence point, the multi-term Caputo derivative is approximated by combining the order reduction technique with the sum-of-exponential approximation to the kernel function appeared in Caputo derivative. The difference scheme can be solved by the recursion, which reduces the storage and computational cost significantly. The obtained scheme is uniquely solvable. The unconditional convergence and stability of the scheme in the discrete H1-norm are proved by the discrete energy method and the convergence accuracy is second-order in time and fourth-order in space. Numerical example illustrates the efficiency of the scheme.