Weak and strong order of convergence of a semidiscrete scheme for the stochastic nonlinear Schrodinger equation

Anne De Bouard; Arnaud Debussche

doi:10.1007/s00245-006-0875-0

Weak and strong order of convergence of a semidiscrete scheme for the stochastic nonlinear Schrodinger equation

Anne De Bouard
, Arnaud Debussche

ENS Paris-Saclay

Research output: Contribution to journal › Article › peer-review

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 1/2 in general and order 1 if the noise is additive. Furthermore, we also prove that the weak order is always 1.

Original language	English
Pages (from-to)	369-399
Number of pages	31
Journal	Applied Mathematics & Optimization
Volume	54
Issue number	3
DOIs	https://doi.org/10.1007/s00245-006-0875-0
Publication status	Published - 1 Nov 2006

Keywords

Nonlinear Schrödinger equations
Numerical schemes
Rate of convergence
Stochastic partial differential equations

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10.1007/s00245-006-0875-0

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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 1/2 in general and order 1 if the noise is additive. Furthermore, we also prove that the weak order is always 1.",

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AU - Debussche, Arnaud

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N2 - 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 1/2 in general and order 1 if the noise is additive. Furthermore, we also prove that the weak order is always 1.

AB - 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 1/2 in general and order 1 if the noise is additive. Furthermore, we also prove that the weak order is always 1.

KW - Nonlinear Schrödinger equations

KW - Numerical schemes

KW - Rate of convergence

KW - Stochastic partial differential equations

UR - https://www.scopus.com/pages/publications/33750308058

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DO - 10.1007/s00245-006-0875-0

M3 - Article

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SN - 0095-4616

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EP - 399

JO - Applied Mathematics & Optimization

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ER -

Weak and strong order of convergence of a semidiscrete scheme for the stochastic nonlinear Schrodinger equation

Abstract

Keywords

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