Numerical procedures for the determination of an unknown coefficient in semi-linear parabolic differential equations

J. R. Cannon, Yanping Lin, Shuzhan Xu

Research output: Journal article publicationJournal articleAcademic researchpeer-review

88 Citations (Scopus)

Abstract

We consider a finite difference approximation to an inverse problem of determining an unknown source parameter p(t) which is a coefficient of the solution u in a linear parabolic equation subject to the specification of the solution u at an internal point along with the usual initial boundary conditions. The backward Euler scheme is studied and its convergence is proved via an application of the discrete maximum principle for a transformed problem. Error estimates For u and p involve numerical differentiation of the approximation to the transformed problem. Some experimental numerical results using the newly proposed numerical procedure are discussed.
Original languageEnglish
Pages (from-to)227-243
Number of pages17
JournalInverse Problems
Volume10
Issue number2
DOIs
Publication statusPublished - 1 Jan 1994
Externally publishedYes

ASJC Scopus subject areas

  • Signal Processing
  • Applied Mathematics
  • Mathematical Physics
  • Theoretical Computer Science
  • Computer Science Applications
  • Statistical and Nonlinear Physics
  • Physics and Astronomy(all)

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