On Tsertsvadze's difference scheme for the Kuramoto-Tsuzuki equation
Journal of Computational and Applied Mathematics
Numerical simulation of coupled nonlinear Schrödinger equation
Mathematics and Computers in Simulation
A linearly implicit conservative scheme for the coupled nonlinear Schrödinger equation
Mathematics and Computers in Simulation
On convergence and stability of a numerical scheme of Coupled Nonlinear Schrödinger Equations
Computers & Mathematics with Applications
Analysis of a symplectic difference scheme for a coupled nonlinear Schrödinger system
Journal of Computational and Applied Mathematics
Journal of Computational and Applied Mathematics
Journal of Computational Physics
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In this article, a finite difference scheme for coupled nonlinear Schrodinger equations is studied. The existence of the difference solution is proved by Brouwer fixed point theorem. With the aid of the fact that the difference solution satisfies two conservation laws, the finite difference solution is proved to be bounded in the discrete L"~ norm. Then, the difference solution is shown to be unique and second order convergent in the discrete L"~ norm. Finally, a convergent iterative algorithm is presented.