Abstract
The present paper is concerned with parabolic differential equations ut-L(x,t;u)=0 where L denotes a quasilinear strongly elliptic operator of second ordr. L(x,t;u)=0 is supposed to be the Euler equation of a corresponding variational problem for which a discrete analogue is constructed. To the resulting semi-discrete problem Crank-Nicolson’s method, a backward differentiation method, and the boundary value method suggested by Greenspan are applied and their convergence is proved.
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Gekeler, E., Gentzsch, W. (1975). Differenzenverfahren for Quasilineare Parabolische Anfangsrandwertaufgaben. In: Numerische Behandlung von Differentialgleichungen. International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série Internationale D’Analyse Numérique, vol 27. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-5532-7_5
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DOI: https://doi.org/10.1007/978-3-0348-5532-7_5
Publisher Name: Birkhäuser, Basel
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