Numerical Solution Of Nonlinear Klein-Gordon-Schr(?)dinger Equations

The nonlinear Klein Gordon Schr(?)dinger(KGS)equations describe a classical model of interaction between nucleon field and meson field.Since the KGS equation is not completely integrable,it is very important to study the numerical solution of KGS equations.In this paper,we mainly study the linear energy conservation scheme and its numerical calculation for the nonlinear KGS equations.A linearized energy-preserve,unconditionally stable and efficient scheme is proposed.In order to overcome the difficulty of the system in designing an effective scheme for KGS equation,some auxiliary variables are utilized to transform the original system into its real form.Based on the invariant energy quadratization approach,an equivalent system is deduced by introducing Lagrange multipliers.Then the efficient and unconditionally stable scheme is designed to discretize the equivalent system.The finite difference method is adopted to discretize in space,and linear implicit energy-preserve scheme to discretize in time for the reduced system.The conservation properties of the semi-discrete scheme and the full-discrete scheme are analyzed,respectively.A numerical analysis of the proposed scheme is presented to illustrate its uniquely solvability and convergence.Numerical examples are provided to validate accuracy,energy conservation law and the stability of our proposed method.