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Highly accurate finite difference method for coupled nonlinear Schrödinger equation. (English) Zbl 1058.65090
Summary: The coupled nonlinear Schrödinger equation models several interesting physical phenomena. It presents a model equation for optical fiber with linear birefringence. In this article, we write a finite difference scheme to solve this equation. The method is fourth-order in space and second-order in time. It is unconditionally stable and extrapolation is used in the temporal direction and this makes the method fourth-order in the two directions, space and time. Many numerical tests have been conducted to display the robustness of the scheme.

MSC:
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
35Q51 Soliton equations
35Q53 KdV equations (Korteweg-de Vries equations)
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