High-Order Difference Scheme for the Solution of Linear Time Fractional Klein–Gordon Equations

摘要

In this article, we apply a high-order difference scheme for the solution of some time fractional partial differential equations (PDEs). The time fractional Cattaneo equation and the linear time fractional Klein–Gordon and dissipative Klein–Gordon equations will be investigated. The time fractional derivative which has been described in the Caputo's sense is approximated by a scheme of order O(τ~(3?α)), 1 < α < 2, and the space derivative is discretized with a fourth-order compact procedure.We will prove the solvability of the proposed method by coefficient matrix property and the unconditional stability and L_∞-convergence with the energy method. Numerical examples demonstrate the theoretical results and the high accuracy of the proposed scheme.