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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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Time discretization in the backward solution of parabolic equations. I
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by Lars Eldén PDF
Math. Comp. 39 (1982), 53-68 Request permission

Abstract:

The problem of solving a parabolic partial differential equation backwards in time by a method related to the Tikhonov-Phillips regularization method is considered. Time discretizations based on Padé approximations of the exponential function are studied, and a priori estimates of the step length are given, which guarantee an almost optimal error bound. The computational efficiency of different discretizations is discussed. Some numerical examples are given. In Part II of this paper we study the backward beam method, and the same error estimates are obtained. A new scheme for time descretization based on Padé approximation is discussed.
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Additional Information
  • © Copyright 1982 American Mathematical Society
  • Journal: Math. Comp. 39 (1982), 53-68
  • MSC: Primary 65M30
  • DOI: https://doi.org/10.1090/S0025-5718-1982-0658214-9
  • MathSciNet review: 658214