Open AccessProper orthogonal decomposition method for Schrödinger equation
Author(s) -
Raimondas Čiegis,
Gerda Jankevičiūtė,
Teresė Leonavičienė
Publication year - 2013
Publication title -
lietuvos matematikos rinkinys
Language(s) - English
Resource type - Journals
eISSN - 2335-898X
pISSN - 0132-2818
DOI - 10.15388/lmr.b.2013.01
Subject(s) - point of delivery , proper orthogonal decomposition , mathematics , gaussian , decomposition , basis (linear algebra) , schrödinger equation , reduction (mathematics) , decomposition method (queueing theory) , wave equation , mathematical analysis , physics , quantum mechanics , geometry , statistics , ecology , agronomy , biology
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.