Some Numerical Studies On Coupled Nonlinear Klein-Gordon Equations

In this article,finite difference method is applied to study the 2-coupled nonlinear Klein-Gordon equations and N-coupled Klein-Gordon equations.Two conserved compact finite difference scheme are proposed for solving the 2-coupled nonlinear Klein-Gordon equations.The first scheme is a nonlinear compact scheme.The second one is a linear compact scheme with a parameter?0((27)?(27))1.Then a nonlinear compact finite difference scheme is investigated to solve the N-coupled Klein-Gordon equations.The conservative property,convergence and stability of the difference solutions are theoretically analyzed.Besides,some iterative algorithms for the nonlinear finite difference scheme are discussed.We prove that our compact difference schemes are convergent in the order ofO(?~2(10)h~4).Due to the difficulty in obtaining the priori estimate from the discrete conservative law,we utilize cut-off function technique to prove the convergence.The numerical results are reported to verify the theoretical analysis.