A compact difference scheme for a two dimensional fractional Klein–Gordon equation with Neumann boundary conditions

In this paper, a high order finite difference scheme for a two dimensional fractional Klein–Gordon equation subject to Neumann boundary conditions is proposed. The difficulty induced by the nonlinear term and the Neumann conditions is carefully handled in the proposed scheme. The stability and convergence of the finite difference scheme are analyzed using the matrix form of the scheme. Numerical examples are provided to demonstrate the theoretical results.