Variable preconditioning in complex Hilbert space and its application to the nonlinear Schrödinger equation

J. Karátson, B. Kovács

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

An iterative method is developed for nonlinear equations in complex Hilbert spaces, extending the method of variable preconditioning defined earlier in real spaces. We derive convergence of our method. The motivating example for this extension is the time-dependent nonlinear Schrödinger equation, where we use our iteration for the time discretization of the problem and test it numerically.

Original languageEnglish
Pages (from-to)449-459
Number of pages11
JournalComputers and Mathematics with Applications
Volume65
Issue number3
DOIs
Publication statusPublished - Feb 2013

Fingerprint

Hilbert spaces
Preconditioning
Nonlinear equations
Nonlinear Equations
Hilbert space
Iteration
Time Discretization
Iterative methods

Keywords

  • Nonlinear elliptic problems
  • Preconditioning
  • Schrödinger equation

ASJC Scopus subject areas

  • Computational Theory and Mathematics
  • Modelling and Simulation
  • Computational Mathematics

Cite this

Variable preconditioning in complex Hilbert space and its application to the nonlinear Schrödinger equation. / Karátson, J.; Kovács, B.

In: Computers and Mathematics with Applications, Vol. 65, No. 3, 02.2013, p. 449-459.

Research output: Contribution to journalArticle

@article{a82f685600f24148a78320645d3959fa,
title = "Variable preconditioning in complex Hilbert space and its application to the nonlinear Schr{\"o}dinger equation",
abstract = "An iterative method is developed for nonlinear equations in complex Hilbert spaces, extending the method of variable preconditioning defined earlier in real spaces. We derive convergence of our method. The motivating example for this extension is the time-dependent nonlinear Schr{\"o}dinger equation, where we use our iteration for the time discretization of the problem and test it numerically.",
keywords = "Nonlinear elliptic problems, Preconditioning, Schr{\"o}dinger equation",
author = "J. Kar{\'a}tson and B. Kov{\'a}cs",
year = "2013",
month = "2",
doi = "10.1016/j.camwa.2012.04.021",
language = "English",
volume = "65",
pages = "449--459",
journal = "Computers and Mathematics with Applications",
issn = "0898-1221",
publisher = "Elsevier Limited",
number = "3",

}

TY - JOUR

T1 - Variable preconditioning in complex Hilbert space and its application to the nonlinear Schrödinger equation

AU - Karátson, J.

AU - Kovács, B.

PY - 2013/2

Y1 - 2013/2

N2 - An iterative method is developed for nonlinear equations in complex Hilbert spaces, extending the method of variable preconditioning defined earlier in real spaces. We derive convergence of our method. The motivating example for this extension is the time-dependent nonlinear Schrödinger equation, where we use our iteration for the time discretization of the problem and test it numerically.

AB - An iterative method is developed for nonlinear equations in complex Hilbert spaces, extending the method of variable preconditioning defined earlier in real spaces. We derive convergence of our method. The motivating example for this extension is the time-dependent nonlinear Schrödinger equation, where we use our iteration for the time discretization of the problem and test it numerically.

KW - Nonlinear elliptic problems

KW - Preconditioning

KW - Schrödinger equation

UR - http://www.scopus.com/inward/record.url?scp=84872601589&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84872601589&partnerID=8YFLogxK

U2 - 10.1016/j.camwa.2012.04.021

DO - 10.1016/j.camwa.2012.04.021

M3 - Article

AN - SCOPUS:84872601589

VL - 65

SP - 449

EP - 459

JO - Computers and Mathematics with Applications

JF - Computers and Mathematics with Applications

SN - 0898-1221

IS - 3

ER -