English

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 exp[±ikx]\exp[\pm ik x]. 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.

Keywords

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)

R2 v1 2026-06-21T20:47:45.115Z