A comparison of regularizations for an illposed problem
Authors:
Karen A. Ames, Gordon W. Clark, James F. Epperson and Seth F. Oppenheimer
Journal:
Math. Comp. 67 (1998), 14511471
MSC (1991):
Primary 35A35, 35R25, 65M30, 65M15
MathSciNet review:
1609682
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Additional Information
Abstract: We consider numerical methods for a ``quasiboundary value'' regularization of the backward parabolic problem given by where is positive selfadjoint and unbounded. The regularization, due to Clark and Oppenheimer, perturbs the final value by adding , where is a small parameter. We show how this leads very naturally to a reformulation of the problem as a secondkind 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. We consider numerical methods for a ``quasiboundary value'' regularization of the backward parabolic problem given by where is positive selfadjoint and unbounded. The regularization, due to Clark and Oppenheimer, perturbs the final value by adding , where is a small parameter. We show how this leads very naturally to a reformulation of the problem as a secondkind 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.
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Additional Information
Karen A. Ames
Affiliation:
Department of Mathematical Sciences, University of Alabama in Huntsville, Huntsville, Alabama 35899
Address at time of publication:
Department of Mathematical Sciences, Virginia Commonwealth University, Richmond, VA 23284
Email:
ames@math.uah.edu
Gordon W. Clark
Affiliation:
Department of Mathematics and Statistics, Mississippi State University, Drawer MA MSU, MS 39762
Address at time of publication:
Department of Mathematical Sciences, Virginia Commonwealth University, Richmond, VA 23284
Email:
gwclark@saturn.vcu.edu
James F. Epperson
Affiliation:
Department of Mathematical Sciences, University of Alabama in Huntsville, Huntsville, Alabama 35899
Email:
epperson@math.uah.edu, seth@math.msstate.edu
Seth F. Oppenheimer
Affiliation:
Department of Mathematics and Statistics, Mississippi State University, Drawer MA MSU, MS 39762
Email:
seth@math.msstate.edu
DOI:
http://dx.doi.org/10.1090/S002557189801014X
PII:
S 00255718(98)01014X
Keywords:
Quasireversibility,
final value problems,
illposed problems,
Freholm equations,
numerical methods
Received by editor(s):
April 17, 1996
Additional Notes:
Partially supported by Army contract DACA 3994K0018 (S.F.O.) and by NSF contract DMS9308121 (K.A.A.)
Article copyright:
© Copyright 1998
American Mathematical Society
