Analysis of finite element method for one-dimensional time-dependent Schrödinger equation on unbounded domain

Jicheng Jin*, Xiaonan WU

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

17 Citations (Scopus)

Abstract

This paper addresses the theoretical analysis of a fully discrete scheme for the one-dimensional time-dependent Schrödinger equation on unbounded domain. We first reduce the original problem into an initial-boundary value problem in a bounded domain by introducing a transparent boundary condition, then fully discretize this reduced problem by applying Crank-Nicolson scheme in time and linear or quadratic finite element approximation in space. By a rigorous analysis, this scheme has been proved to be unconditionally stable and convergent, its convergence order has also be obtained. Finally, two numerical examples are performed to show the accuracy of the scheme.

Original languageEnglish
Pages (from-to)240-256
Number of pages17
JournalJournal of Computational and Applied Mathematics
Volume220
Issue number1-2
DOIs
Publication statusPublished - 15 Oct 2008

Scopus Subject Areas

  • Computational Mathematics
  • Applied Mathematics

User-Defined Keywords

  • Artificial boundary
  • Finite element method
  • Schrödinger equation

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