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Mathematics of Computation

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



On the numerical computation of parabolic problems for preceding times

Authors: B. L. Buzbee and Alfred Carasso
Journal: Math. Comp. 27 (1973), 237-266
MSC: Primary 65M30
MathSciNet review: 0368448
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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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Keywords: Improperly posed problems, backward parabolic equations, time-dependent coefficients, finite-difference scheme, jury-procedure, the backward beam equation, block Gaussian elimination, method of lines, variable domain operator, smoothing by growing diffusion coefficient, convexity inequalities for parabolic equations, long-time backward computation, matrix decomposition code
Article copyright: © Copyright 1973 American Mathematical Society

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