On the Cauchy problem for the one-dimensional heat equation

Author:
F. Ginsberg

Journal:
Math. Comp. **17** (1963), 257-269

MSC:
Primary 35.78

DOI:
https://doi.org/10.1090/S0025-5718-1963-0162064-8

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 *x* -- *t* 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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DOI:
https://doi.org/10.1090/S0025-5718-1963-0162064-8

Article copyright:
© Copyright 1963
American Mathematical Society