High accuracy power series method for solving scalar, vector, and inhomogeneous nonlinear Schrödinger equations

L. Al Sakkaf, U. Al Khawaja

Research output: Contribution to journalArticlepeer-review

5 Citations (Scopus)

Abstract

We develop a high accuracy power series method for solving partial differential equations with emphasis on the nonlinear Schrödinger equations. The accuracy and computing speed can be systematically and arbitrarily increased to orders of magnitude larger than those of other methods. Machine precision accuracy can be easily reached and sustained for long evolution times within rather short computing time. In-depth analysis and characterisation for all sources of error are performed by comparing the numerical solutions with the exact analytical ones. Exact and approximate boundary conditions are considered and shown to minimise errors for solutions with finite background. The method is extended to cases with external potentials and coupled nonlinear Schrödinger equations.

Original languageEnglish
Pages (from-to)11803-11824
Number of pages22
JournalAlexandria Engineering Journal
Volume61
Issue number12
DOIs
Publication statusPublished - Dec 2022

Keywords

  • Finite difference
  • Nonlinear Schrödinger equation
  • Power series
  • Soliton

ASJC Scopus subject areas

  • General Engineering

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