Spurious localized highest-frequency modes in Schr\"odinger-type equations solved by finite-difference methods
Mathematical Physics
2012-04-12 v1 math.MP
Pattern Formation and Solitons
Abstract
High-frequency solutions of one or several Schr\"odinger-type equations are well known to differ very little from the plane wave solutions . 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.
Cite
@article{arxiv.1204.2334,
title = {Spurious localized highest-frequency modes in Schr\"odinger-type equations solved by finite-difference methods},
author = {Taras I. Lakoba},
journal= {arXiv preprint arXiv:1204.2334},
year = {2012}
}
Comments
4 pages, 6 figure panels (2 figures)