Spurious localized highest-frequency modes in Schrödinger-type equations solved by finite-difference methods

DOI10.1016/J.CAM.2012.12.015zbMATH Open1262.65088arXiv1204.2334OpenAlexW2963469939MaRDI QIDQ1947494

Taras I. Lakoba

Publication date: 22 April 2013

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Abstract: High-frequency solutions of one or several Schr"odinger-type equations are well known to differ very little from the plane wave solutions $exp[pmikx]$. That is, the potential terms impact the envelope of a high-frequency plane wave by only a small amount. However, when such equations are solved by a finite-difference method, the highest-frequency solutions may, under certain conditions, turn out to be localized. In this letter we explain this numerical artifact.

Full work available at URL: https://arxiv.org/abs/1204.2334

zbMATH Keywords

finite-difference methodseigenvalue problemshigh-frequency modes

Mathematics Subject Classification ID

Finite difference and finite volume methods for ordinary differential equations (65L12)

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