Convergence of difference scheme for heat equation in unbounded domains using artificial boundary conditions

Xiaonan WU*, Zhi Zhong Sun

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

45 Citations (Scopus)

Abstract

The finite difference solution of one-dimensional heat conduction equation in unbounded domains is considered. An artificial boundary is introduced to make the computational domain finite. On the artificial boundary an exact boundary condition is applied to reduce the original problem to an initial-boundary value problem. A finite difference scheme is constructed by the method of reduction of order. It is proved that the finite difference scheme is uniquely solvable, unconditionally stable and convergent with the order 2 in space and the order 3/2 in time under an energy norm. A numerical example demonstrates the theoretical results.

Original languageEnglish
Pages (from-to)261-277
Number of pages17
JournalApplied Numerical Mathematics
Volume50
Issue number2
DOIs
Publication statusPublished - Aug 2004

Scopus Subject Areas

  • Numerical Analysis
  • Computational Mathematics
  • Applied Mathematics

User-Defined Keywords

  • Artificial boundary condition
  • Finite difference
  • Heat equation
  • Unbounded domain

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