О повышении точности численных решений уравнения Гинзбурга - Ландау

Translated title of the contribution: Improving the accuracy for numerical solutions of the Ginzburg - Landau equation

Research output: Contribution to journalArticlepeer-review

Abstract

Increasing the order of accuracy for difference methods is an actual problem in nonlinear fiber optics. Computations, which use higher than the fourth order of accuracy by the direct construction of complex circuits on extended templates pose the complication of the system matrix and difficulties in setting additional boundary conditions. In addition, with this approach, there is no simultaneous increase in accuracy for the evolutionary variable. In this paper, we consider an alternative way, namely, application of the Richardson extrapolation, which reduces to construction of suitable linear combinations for solutions on various grids. This method allows improving the order of accuracy for both variables, while avoiding problems associated with the complication of templates, implementation of algorithms and setting additional boundary conditions. Double corrections are also considered to further improve accuracy. The technique was tested on exact solutions of the Ginzburg - Landau equation.

Translated title of the contributionImproving the accuracy for numerical solutions of the Ginzburg - Landau equation
Original languageRussian
Article number4
Pages (from-to)45-57
Number of pages13
JournalJournal of Computational Technologies
Volume25
Issue number4
DOIs
Publication statusPublished - Jun 2020

Keywords

  • Ginzburg - Landau equation
  • Order of accuracy
  • Richardson extrapolation
  • Runge correction
  • Schrodinger equation

OECD FOS+WOS

  • 1.02 COMPUTER AND INFORMATION SCIENCES
  • 1.01 MATHEMATICS

State classification of scientific and technological information

  • 27 MATHEMATICS

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