A comparison of regularizations for an ill-posed problem

Karen A. Ames, Gordon W. Clark, James F. Epperson, Seth F. Oppenheimer

Research output: Contribution to journalArticlepeer-review

76 Scopus citations


We consider numerical methods for a "quasi-boundary value" regularization of the backward parabolic problem given by { ut + Au = 0, 0 < t < T { u(T) = f, where A is positive self-adjoint and unbounded. The regularization, due to Clark and Oppenheimer, perturbs the final value u(T) by adding αu(0). where α is a small parameter. We show how this leads very naturally to a reformulation of the problem as a second-kind Fredholm integral equation, which can be very easily approximated using methods previously developed by Ames and Epperson. Error estimates and examples are provided. We also compare the regularization used here with that from Ames and Epperson.

Original languageEnglish (US)
Pages (from-to)1451-1471
Number of pages21
JournalMathematics of Computation
Issue number224
StatePublished - Oct 1998
Externally publishedYes


  • Final value problems
  • Freholm equations
  • Ill-posed problems
  • Numerical methods
  • Quasi-reversibility

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Computational Mathematics
  • Applied Mathematics


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