Time discretization in the backward solution of parabolic equations. I

Author:
Lars Eldén

Journal:
Math. Comp. **39** (1982), 53-68

MSC:
Primary 65M30

DOI:
https://doi.org/10.1090/S0025-5718-1982-0658214-9

MathSciNet review:
658214

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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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DOI:
https://doi.org/10.1090/S0025-5718-1982-0658214-9

Article copyright:
© Copyright 1982
American Mathematical Society