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A linearized finite-difference scheme for the numerical solution of the nonlinear cubic Schrödinger equation

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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Correspondence to A. G. Bratsos.

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Bratsos, A.G. A linearized finite-difference scheme for the numerical solution of the nonlinear cubic Schrödinger equation. Korean J. Comput. & Appl. Math. 8, 459–467 (2001). https://doi.org/10.1007/BF02941979

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  • DOI: https://doi.org/10.1007/BF02941979

AMS Mathematics Subject Classification

  • 65J15
  • 47H17
  • 49D15

Key words and Phrases

  • Nonlinear cubic Schrödinger equation
  • soliton
  • finite-difference method