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

Weak and Strong Order of Convergence of a Semidiscrete Scheme for the Stochastic Nonlinear... 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Mathematics and Optimization Springer Journals

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

, Volume 54 (3) – Nov 1, 2006
31 pages

/lp/springer_journal/weak-and-strong-order-of-convergence-of-a-semidiscrete-scheme-for-the-cetfcJR2QR
Publisher
Springer-Verlag
Subject
Mathematics; Systems Theory, Control; Calculus of Variations and Optimal Control; Optimization; Mathematical and Computational Physics; Mathematical Methods in Physics; Numerical and Computational Methods
ISSN
0095-4616
eISSN
1432-0606
D.O.I.
10.1007/s00245-006-0875-0
Publisher site
See Article on Publisher Site

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.

Journal

Applied Mathematics and OptimizationSpringer Journals

Published: Nov 1, 2006

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