A new fourth-order energy dissipative difference method for high-dimensional nonlinear fractional generalized wave equations

摘要

In this paper, a new energy dissipative fourth-order difference scheme for the high-dimensional nonlinear fractional generalized wave equations is constructed. Then, the discrete energy dissipation property of the system is exhibited in detail. Next, we prove that the proposed scheme is uniquely solvable. By the discrete energy method, it is shown that the proposed scheme achieves the optimal convergence rate of O(Delta t(2) + h(x)(4) + h(y)(4)) in the discrete L-2-norm, and is unconditionally stable. Besides, the presented convergence analysis is unconditional for the time step size in terms of space mesh sizes. Lastly, some numerical results are given to illustrate the physical effects of the nonzero damping terms and support our theoretical analysis. (C) 2019 Elsevier B.V. All rights reserved.