Convergence rates for dispersive approximation schemes to nonlinear Schrodinger equations

Ignat LI, Zuazua E (2012)

Publication Type: Journal article

Publication year: 2012

Journal

Journal De Mathematiques Pures Et Appliquees Elsevier

Book Volume: 98

Pages Range: 479-517

Journal Issue: 5

DOI: 10.1016/j.matpur.2012.01.001

Abstract

This article is devoted to the analysis of the convergence rates of several numerical approximation schemes for linear and nonlinear Schrodinger equations on the real line. Recently, the authors have introduced viscous and two-grid numerical approximation schemes that mimic at the discrete level the so-called Strichartz dispersive estimates of the continuous Schrodinger equation. This allows to guarantee the convergence of numerical approximations for initial data in L-2(R), a fact that cannot be proved in the nonlinear setting for standard conservative schemes unless more regularity of the initial data is assumed. In the present article we obtain explicit convergence rates and prove that dispersive schemes fulfilling the Strichartz estimates are better behaved for H-s (R) data if 0 < s < 1/2. Indeed, while dispersive schemes ensure a polynomial convergence rate, non-dispersive ones only yield logarithmic ones. (C) 2012 Elsevier Masson SAS. All rights reserved.

Authors with CRIS profile

Enrique Zuazua Iriondo

Involved external institutions

Romanian Academy / Academia Română RO Romania (RO) Basque Center of Applied Mathematics (BCAM) ES Spain (ES)

How to cite

APA:

Ignat, L.I., & Zuazua, E. (2012). Convergence rates for dispersive approximation schemes to nonlinear Schrodinger equations. Journal De Mathematiques Pures Et Appliquees, 98(5), 479-517. https://dx.doi.org/10.1016/j.matpur.2012.01.001

MLA:

Ignat, Liviu I., and Enrique Zuazua. "Convergence rates for dispersive approximation schemes to nonlinear Schrodinger equations." Journal De Mathematiques Pures Et Appliquees 98.5 (2012): 479-517.

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