Skip to main content
SpringerLink
Log in

Weak and Strong Order of Convergence of a Semidiscrete Scheme for the Stochastic Nonlinear Schrodinger Equation

  • Published:
Applied Mathematics and Optimization Submit manuscript

Abstract

In this article we analyze the error of a semidiscrete scheme for the stochastic nonlinear Schrodinger equation with power nonlinearity. We consider supercritical or subcritical nonlinearity and the equation can be either focusing or defocusing. Allowing sufficient spatial regularity we prove that the numerical scheme has strong order \(\frac 12\) in general and order 1 if the noise is additive. Furthermore, we also prove that the weak order is always 1.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

Author information

Authors and Affiliations

  1. CNRS, Laboratoire de Mathematiques, Universite de Paris-Sud, 91405, Orsay Cedex, France

    Anne de Bouard

  2. IRMAR et ENS de Cachan, Antenne de Bretagne, Campus de Ker Lann, Av. R. Schuman, 35170, Bruz, France

    Arnaud Debussche

Authors
  1. Anne de Bouard
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Arnaud Debussche
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to Anne de Bouard or Arnaud Debussche.

Rights and permissions

Reprints and permissions

About this article

Cite this article

de Bouard, A., Debussche, A. Weak and Strong Order of Convergence of a Semidiscrete Scheme for the Stochastic Nonlinear Schrodinger Equation. Appl Math Optim 54, 369–399 (2006). https://doi.org/10.1007/s00245-006-0875-0

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00245-006-0875-0

Keywords

Search

Navigation