2007 | OriginalPaper | Buchkapitel
On the Sign-Stability of the Finite Difference Solutions of One-Dimensional Parabolic Problems
verfasst von : Róbert Horváth
Erschienen in: Numerical Methods and Applications
Verlag: Springer Berlin Heidelberg
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In the numerical solutions of partial differential equations, the preservation of the qualitative properties of the original problem is a more and more important requirement. For 1D parabolic equations, one of this properties is the so-called sign-stability: the number of sign-changes of the solution cannot increase in time. This property is investigated for the finite difference solutions, and a sufficient condition is given to guarantee the numerical sign-stability. We prove sufficient conditions for the sign-stability and sign-unstability of tridiagonal matrices.