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New conservative difference schemes for a coupled nonlinear Schrödinger system. (English) Zbl 1205.65242
The authors numerically analyze two conservative finite difference schemes for solving a coupled nonlinear Schrödinger system with mass and energy as conserved quantities. One scheme is a nonlinear implicit two-level scheme. The other scheme is a linear three-level scheme. Second-order convergence and unconditional stability of the linear scheme are established by means of an induction argument and the discrete energy method. Numerical experiments show the efficiency of the uncoupled linear scheme which can be run with the use of parallel computation.
MSC:
65M06Finite difference methods (IVP of PDE)
35Q55NLS-like (nonlinear Schrödinger) equations
65M12Stability and convergence of numerical methods (IVP of PDE)
65Y05Parallel computation (numerical methods)
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