Error control for time-splitting spectral approximations of the semiclassical Schrödinger equation

Irene Kyza; Charalambos Makridakis; Michael Plexousakis

doi:10.1093/imanum/drp044

Error control for time-splitting spectral approximations of the semiclassical Schrödinger equation

Irene Kyza
, Charalambos Makridakis^*
, Michael Plexousakis

^*Corresponding author for this work

Applied Mathematics

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

Abstract

We prove a posteriori error estimates of optimal order in the L ^∞(L²)-norm for time-splitting spectral methods applied to the linear Schrödinger equation in the semiclassical regime. The a posteriori error estimates are obtained by considering an appropriate extension in time of the numerical schemes and using energy techniques. Numerical experiments are presented that confirm our theoretical results.

Original language	English
Pages (from-to)	416-441
Number of pages	26
Journal	IMA Journal of Numerical Analysis
Volume	31
Issue number	2
DOIs	https://doi.org/10.1093/imanum/drp044
Publication status	Published - Apr 2011

Keywords

a posteriori estimates
Schrödinger equation
time-splitting spectral methods

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title = "Error control for time-splitting spectral approximations of the semiclassical Schr{\"o}dinger equation",

abstract = "We prove a posteriori error estimates of optimal order in the L ∞(L2)-norm for time-splitting spectral methods applied to the linear Schr{\"o}dinger equation in the semiclassical regime. The a posteriori error estimates are obtained by considering an appropriate extension in time of the numerical schemes and using energy techniques. Numerical experiments are presented that confirm our theoretical results.",

keywords = "a posteriori estimates, Schr{\"o}dinger equation, time-splitting spectral methods",

author = "Irene Kyza and Charalambos Makridakis and Michael Plexousakis",

year = "2011",

month = apr,

doi = "10.1093/imanum/drp044",

language = "English",

volume = "31",

pages = "416--441",

journal = "IMA Journal of Numerical Analysis",

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T1 - Error control for time-splitting spectral approximations of the semiclassical Schrödinger equation

AU - Kyza, Irene

AU - Makridakis, Charalambos

AU - Plexousakis, Michael

PY - 2011/4

Y1 - 2011/4

N2 - We prove a posteriori error estimates of optimal order in the L ∞(L2)-norm for time-splitting spectral methods applied to the linear Schrödinger equation in the semiclassical regime. The a posteriori error estimates are obtained by considering an appropriate extension in time of the numerical schemes and using energy techniques. Numerical experiments are presented that confirm our theoretical results.

AB - We prove a posteriori error estimates of optimal order in the L ∞(L2)-norm for time-splitting spectral methods applied to the linear Schrödinger equation in the semiclassical regime. The a posteriori error estimates are obtained by considering an appropriate extension in time of the numerical schemes and using energy techniques. Numerical experiments are presented that confirm our theoretical results.

KW - a posteriori estimates

KW - Schrödinger equation

KW - time-splitting spectral methods

UR - https://www.scopus.com/pages/publications/79953675709

U2 - 10.1093/imanum/drp044

DO - 10.1093/imanum/drp044

M3 - Article

AN - SCOPUS:79953675709

SN - 0272-4979

VL - 31

SP - 416

EP - 441

JO - IMA Journal of Numerical Analysis

JF - IMA Journal of Numerical Analysis

IS - 2

ER -

Error control for time-splitting spectral approximations of the semiclassical Schrödinger equation

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Keywords

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