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

Irene Kyza; Charalambos Makridakis; Michael Plexousakis

doi:10.1093/imanum/drp044

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

Irene Kyza, Charalambos Makridakis, Michael Plexousakis

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

7 Citations (Scopus)

Abstract

We prove a posteriori error estimates of optimal order in the L(infinity)(L(2))-norm for time-splitting spectral methods applied to the linear Schrodinger 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
time-splitting spectral methods
Schrodinger equation

Access to Document

10.1093/imanum/drp044

Cite this

@article{241f48b9576e42e49f9fdc343c6b6888,

title = "Error control for time-splitting spectral approximations of the semiclassical Schrodinger equation",

abstract = "We prove a posteriori error estimates of optimal order in the L(infinity)(L(2))-norm for time-splitting spectral methods applied to the linear Schrodinger 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, time-splitting spectral methods, Schrodinger equation",

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",

issn = "0272-4979",

publisher = "Oxford University Press",

number = "2",

}

TY - JOUR

T1 - Error control for time-splitting spectral approximations of the semiclassical Schrodinger 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(infinity)(L(2))-norm for time-splitting spectral methods applied to the linear Schrodinger 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(infinity)(L(2))-norm for time-splitting spectral methods applied to the linear Schrodinger 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 - time-splitting spectral methods

KW - Schrodinger equation

U2 - 10.1093/imanum/drp044

DO - 10.1093/imanum/drp044

M3 - Article

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 Schrodinger equation

Abstract

Keywords

Access to Document

Fingerprint

Cite this