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- W2088937072 abstract "A method for solution of parabolic PDE by means of interpolation of the differential operators in two dimensions is described. The method is developed on the basis of previously published methods for solution of ordinary differential equations by orthogonal collocation. It is shown to be highly economical and very stable in comparison with the conventional Crank—Nicolson or with explicit methods such as the Runge—Kutta 4th order method. The linear heat equation is used to illustrate the principle of the method and to discuss its convergence properties. Une méthode permettant de résoudre la parabole PDE au moyen de l'interpolation des opérateurs différentiels dans les deux dimensions est décrite dans cet ouvrage. La méthode est basée sur le principe des méthodes précédemment publiées et relatives à lasolution des équations différentielles ordinaires par une collocation orthogonale. On démontre que cette méthode est particulièrement économique et très stable, par comparaison à la méthode Crank—Nicholson ou aux méthodes explicites, telles que la méthode Runge—Kutta — une méthode de 4 ème ordre. L'équation de chaleur linéaire est utilisée pour illustrer le principe de la méthode et discuter ses propriétés de convergence. Es wird eine Methode für die Lösung parabolischer, partieller Differentialgleichungen durch Interpolierung der Differentialoperatoren in zwei Dimensionen beschrieben. Die Methode wurde auf Grund früher beschriebener Methoden für die Lösung gewöhnlicher Differentialgleichungen durch orthogonale Anordnung entwickelt. Es wird gezeigt, dass diese Methode im Vergleich mit der klassischen Crank—Nicholson oder mit expliziten Methoden wie der Runge—Kutta Methode 4. Ordnung äusserst wirtschaftlich und sehr stabil ist. Die lineare Wärmegleichung wird verwendet um das Prinzip der Methode zu erläutern und ihre Konvergenzeigenschaften zu behandeln." @default.
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- W2088937072 title "Solution of parabolic partial differential equations by a double collocation method" @default.
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