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On the Cauchy problem for the one-dimensional heat equation

Author: F. Ginsberg
Journal: Math. Comp. 17 (1963), 257-269
MSC: Primary 35.78
MathSciNet review: 0162064
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Abstract: In this paper we show that the Cauchy problem for the one-dimensional heat equation, though non-well posed in the sense of Hadamard, can be solved numerically. It is shown that if we admit as solutions functions for which an a priori bound is assumed in some finite rectangle in xt space then the solution depends Hölder continuously upon the given Cauchy data. The specific numerical scheme developed also exhibits the Hölder continuity so that we are sure of a meaningful numerical method.

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Article copyright: © Copyright 1963 American Mathematical Society