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)


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.


Parabolic Problem Tridiagonal Matrix Tridiagonal Matrice Discrete Maximum Principle Finite Difference Solution 
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© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

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

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