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Some integral properties of the heat equation

✍ Scribed by R. Horváth

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
496 KB
Volume
42
Category
Article
ISSN
0898-1221

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✦ Synopsis

In this paper, we consider the one-dimensional heat conduction equation on the interval [0, 1]. We investigate the integrals of the solution u with respect to the space and time variables and the equivalents of the integrals in the numerical solution. We give the properties of the functions E :

R+O --* R, E(t) = f~) u(x, t) dx, and F: [0, 1] --* R, f(x) = f~ u(x, t) dr. We perform the numerical solution applying the so-called (a, 0)-method [1]. We show that with the additional conditions of the nonnegativity preservation and maximum norm contractivity [2], similar statements are valid as in the continuous case.

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