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

  • A. G. Bratsos
Article
  • 247 Downloads

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.

AMS Mathematics Subject Classification

65J15 47H17 49D15 

Key words and Phrases

Nonlinear cubic Schrödinger equation soliton finite-difference method 

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Copyright information

© Korean Society for Computational and Applied Mathematics 2001

Authors and Affiliations

  1. 1.Department of MathematicsTechnological Educational Institution (T.E.I.) of AthensAthensGreece

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