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On the Sign-Stability of Finite Difference Solutions of Semilinear Parabolic Problems

  • Róbert Horváth
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5434)

Abstract

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.

Keywords

Parabolic Problem Tridiagonal Matrix Tridiagonal Matrice Discrete Maximum Principle Finite Difference Solution 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Róbert Horváth
    • 1
  1. 1.Budapest University of Technology and EconomicsBudapestHungary

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