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Compact finite difference schemes with high accuracy for one-dimensional nonlinear Schrödinger equation. (English) Zbl 1229.81011
Summary: In this paper, two compact finite difference schemes are presented for the numerical solution of the one-dimensional nonlinear Schrödinger equation. The discrete L 2 -norm error estimates show that convergence rates of the present schemes are of order O(h 4 +τ 2 ). Numerical experiments on some model problems show that the present schemes preserve the conservation laws of charge and energy and are of high accuracy.
81-08Computational methods (quantum theory)
81Q05Closed and approximate solutions to quantum-mechanical equations
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