Summary
The problem of determining numerically a positive solution u(x, t) of the equation ut = uxx for - T ≦ t ≦ 0 from approximate values of u(x, 0) = f(x) is discussed. For a particular computational scheme estimates for the error are derived, which depend on t, T, the maximum error s in the approximation for f, and on the maximum of f. It turns out that although the problem is incorrectly set in the sense of HADAMARD a satisfactory numerical solution can be obtained due to the a priori assumption u ≧ 0.
This work was performed under the sponsorship of the Office of Naval Research
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References
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To Mauro Picone on his 70th birth day.
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© 1985 Springer Science+Business Media New York
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John, F. (1985). Numerical solution of the equation of heat conduction for preceding times. In: Moser, J. (eds) Fritz John. Contemporary Mathematicians. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-5406-5_30
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DOI: https://doi.org/10.1007/978-1-4612-5406-5_30
Publisher Name: Birkhäuser, Boston, MA
Print ISBN: 978-1-4612-5408-9
Online ISBN: 978-1-4612-5406-5
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