@article{kraaijevanger1992,
abstract = {In this paper we present a necessary and sufficient condition for maximum norm contractivity of a large class of discretization methods for solving the heat equation. Specializing this result for the well-known Crank-Nicolson method we arrive at the criterion DELTA-t/(DELTA-x)2 less-than-or-equal-to 3/2, which is less restrictive than the weakest presently available sufficient condition DELTA-t/(DELTA-x)2 less-than-or-equal-to 1. A comparison is made with other stability criteria and with sufficient conditions obtained by Spijker (1983, 1985) which are based on the concept of absolute monotonicity. The theoretical results are illustrated with several examples, among which the construction of some optimal explicit schemes.},
author = {Kraaijevanger, J. F. B. M.},
journal = {Applied Numerical Mathematics},
keywords = {ODE solver,SSP},
mendeley-tags = {ODE solver,SSP},
pages = {475--492},
title = {{MAXIMUM NORM CONTRACTIVITY OF DISCRETIZATION SCHEMES FOR THE HEAT-EQUATION}},
volume = {9},
year = {1992}
}

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