Abstract
In this paper, several splitting methods are discussed which can be used to solve fourth order parabolic partial differential equations that are given in some suitable first order system form. The methods are generalisations of splitting methods for (second order) parabolic PDE's. For all methods which are considered, stability or instability is studied for problems in 2 and in 3 or more spatial dimensions.
Zusammenfassung
In dieser Arbeit werden mehrere Splitting-Methoden diskutiert, welche zur Lösung von parabolischen partiellen Differentialgleichungen vierter Ordnung benützt werden können, welche in Form eines Systems erster Ordnung geschrieben sind. Die Methoden sind Verallgemeinerungen von Splitting-Methoden für parabolische Gleichungen zweiter Ordnung. Für alle betrachteten Methoden werden Stabilitätsuntersuchungen angestellt für den Fall von 2, 3 und mehr Raumdimensionen.
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ter Maten, E.J.W. Splitting methods for fourth order parabolic partial differential equations. Computing 37, 335–350 (1986). https://doi.org/10.1007/BF02251091
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DOI: https://doi.org/10.1007/BF02251091