A linearized finite-difference scheme for the numerical solution of the nonlinear cubic Schrödinger equation |
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Authors: | A G Bratsos |
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Institution: | 1. Department of Mathematics, Technological Educational Institution (T.E.I.) of Athens, 122 10 Egaleo, Athens, Greece
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Abstract: | A linearized finite-difference scheme is used to transform the initial/boundary-value problem associated with the nonlinear Schrödinger equation into a linear algebraic system. This method is developed by re placing the time and the space partial derivatives by parametric finite-difference re placements and the nonlinear term by an appropriate parametric linearized scheme based on Taylor’s expansion. The resulting finite-difference method is analysed for stability and convergence. The results of a number of numerical experiments for the single-soliton wave are given. |
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