The stability and convergence of a difference scheme for the Schrödinger equation on an infinite domain by using artificial boundary conditions

Zhi Zhong Sun*, Xiaonan WU

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

31 Citations (Scopus)

Abstract

This paper is concerned with the numerical solution to the Schrödinger equation on an infinite domain. Two exact artificial boundary conditions are introduced to reduce the original problem into an initial boundary value problem with computational domain. Then, a fully discrete difference scheme is derived. The truncation errors are analyzed in detail. The unique solvability, stability and convergence with the convergence order of O(h3/23/2 h-1/2) are proved by the energy method. A numerical example is given to demonstrate the accuracy and efficiency of the proposed method. As a special case, the stability and convergence of the difference scheme proposed by Baskakov and Popov in 1991 is obtained.

Original languageEnglish
Pages (from-to)209-223
Number of pages15
JournalJournal of Computational Physics
Volume214
Issue number1
DOIs
Publication statusPublished - 1 May 2006

Scopus Subject Areas

  • Numerical Analysis
  • Modelling and Simulation
  • Physics and Astronomy (miscellaneous)
  • Physics and Astronomy(all)
  • Computer Science Applications
  • Computational Mathematics
  • Applied Mathematics

User-Defined Keywords

  • Convergence
  • Finite difference
  • Schrödinger equation
  • Solvability
  • Stability

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