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Mathematics of Computation

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Difference schemes for degenerate parabolic equations

Author: E. A. Socolovsky
Journal: Math. Comp. 47 (1986), 411-420
MSC: Primary 65M10
MathSciNet review: 856694
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Abstract: Diagonal dominant implicit-difference schemes approximating a porous media type class of multidimensional nonlinear equations are shown to generate semigroups in an approximate $ {L^1}$-space, and the rate of convergence to the semigroup solution in $ {L^1}$ is given. The numerical schemes proposed by Berger et al. in [4] are described and a proof of convergence for the fully discrete algorithms is outlined. Numerical experiments are discussed.

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Keywords: Difference schemes, degenerate nonlinear parabolic equations, nonlinear semigroups
Article copyright: © Copyright 1986 American Mathematical Society

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