Maximum norm contractivity in the numerical solution of the one-dimensional heat equation
Applied Numerical Mathematics
Discrete Maximum Principle and Adequate Discretizations of Linear Parabolic Problems
SIAM Journal on Scientific Computing
On the Sign-Stability of Finite Difference Solutions of Semilinear Parabolic Problems
Numerical Analysis and Its Applications
Discrete maximum principle for linear parabolic problems solved on hybrid meshes
Applied Numerical Mathematics
On the Sign-Stability of Finite Difference Solutions of Semilinear Parabolic Problems
Numerical Analysis and Its Applications
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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.