STABLE EXPLICIT SCHEMES FOR EQUATIONS OF THE SCHROEDINGER TYPE.

Tony F. Chan*, Ding Lee, Longjun Shen

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

30 Scopus citations

Abstract

Most conventional explicit finite difference schemes, e. g. Euler's scheme, for solving the parabolic equation of Schroedinger type u//t equals iu//x//x are unconditionally unstable. This difficulty can be overcome by introducing a dissipative term to the conventional explicit schemes. Based on this approach, we derive a class of new explicit finite difference schemes which are conditionally stable, spans two time levels and are O(k, h**2) accurate. We also determine the schemes from this class that have the least restrictive stability requirements. It is interesting to note that the analog of the Lax-Wendroff scheme is unstable.

Original languageEnglish (US)
Pages (from-to)274-281
Number of pages8
JournalSIAM Journal on Numerical Analysis
Volume23
Issue number2
DOIs
StatePublished - Jan 1 1986
Externally publishedYes

ASJC Scopus subject areas

  • Numerical Analysis

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