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On the sign-stability of finite difference solutions of semilinear parabolic problems. (English) Zbl 1233.65057

Margenov, Svetozar (ed.) et al., Numerical analysis and its applications. 4th international conference, NAA 2008, Lozenetz, Bulgaria, June 16–20, 2008. Revised selected papers. Berlin: Springer (ISBN 978-3-642-00463-6/pbk). Lecture Notes in Computer Science 5434, 305-313 (2009).
Summary: The sign-stability property is one of the important qualitative properties of the one-dimensional heat conduction equation, or more generally, of one-dimensional parabolic problems. This property means that the number of the spatial sign-changes of the solution function cannot increase in time. In this paper, sufficient conditions will be given that guarantee the fulfillment of a numerical analogue of the sign-stability for the finite difference solution of a semilinear parabolic problem. The results are demonstrated on a numerical test problem.
For the entire collection see [Zbl 1157.65002].

MSC:

65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
35K58 Semilinear parabolic equations
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