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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

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On the numerical computation of parabolic problems for preceding times
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by B. L. Buzbee and Alfred Carasso PDF
Math. Comp. 27 (1973), 237-266 Request permission

Abstract:

We develop and analyze a general procedure for computing selfadjoint parabolic problems backwards in time, given an a priori bound on the solutions. The method is applicable to mixed problems with variable coefficients which may depend on time. We obtain error bounds which are naturally related to certain convexity inequalities in parabolic equations. In the time-dependent case, our difference scheme discerns three classes of problems. In the most severe case, we recover a convexity result of Agmon and Nirenberg. We illustrate the method with a numerical experiment.
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Additional Information
  • © Copyright 1973 American Mathematical Society
  • Journal: Math. Comp. 27 (1973), 237-266
  • MSC: Primary 65M30
  • DOI: https://doi.org/10.1090/S0025-5718-1973-0368448-3
  • MathSciNet review: 0368448