Proper orthogonal decomposition method for Schrödinger equation
Articles
Raimondas Čiegis
Vilniaus Gedimino technikos universitetas
Gerda Jankevičiūtė
Vilniaus Gedimino technikos universitetas
Teresė Leonavičienė
Vilniaus Gedimino technikos universitetas
Published 2013-12-20
https://doi.org/10.15388/LMR.B.2013.01
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Keywords

one-dimensional Schrödinger equation
numerical methods
proper orthogonal decomposition method

How to Cite

Čiegis R., Jankevičiūtė G. and Leonavičienė T. (2013) “Proper orthogonal decomposition method for Schrödinger equation”, Lietuvos matematikos rinkinys, 54(B), pp. 1–5. doi: 10.15388/LMR.B.2013.01.

Abstract

In this paper we consider the proper orthogonal decomposition (POD) method for one-dimensional Schrödinger equation. We begin of the review of basic ideas of POD. Later this method is applied to study the linear Schrödinger equation. The generation of optimal basis using POD and model reduction questions are discussed. Also the errors between the POD approximate solutions and the exact problems solutions are calculated. The results of two numerical examples for standing and travelling Gaussian wave are presented and analyzed.

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