Comments on high-order integrators embedded within integral deferred correction methods
نویسندگان
چکیده
منابع مشابه
Comments on High Order Integrators Embedded within Integral Deferred Correction Methods
Spectral deferred correction (SDC) methods for solving ordinary differential equations (ODEs) were introduced by Dutt, Greengard and Rokhlin, [3]. In this paper, we study the properties of these integral deferred correction methods, constructed using high order integrators in the prediction and correction loops, and various distributions of quadrature nodes. The smoothness of the error vector a...
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Spectral deferred correction (SDC) methods for solving ordinary differential equations (ODEs) were introduced by Dutt, Greengard and Rokhlin [5]. It was shown in [5] that SDC methods can achieve arbitrary high order accuracy and possess nice stability properties. Their SDC methods are constructed with low order integrators, such as forward Euler or backward Euler, and are able to handle stiff a...
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Integral deferred correction (IDC) methods have been shown to be an efficient way to achieve arbitrary high order accuracy and possess good stability properties. In this paper, we construct high order operator splitting schemes using the IDC procedure to solve initial value problems (IVPs). We present analysis to show that the IDC methods can correct for both the splitting and numerical errors,...
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It has been demonstrated that spectral deferred correction (SDC) methods can achieve arbitrary high order accuracy and possess good stability properties. There have been some recent interests in using high-order Runge-Kutta methods in the prediction and correction steps in the SDC methods, and higher order rate of convergence is obtained provided that the quadrature nodes are uniform. The assum...
متن کاملOn the order of deferred correction
New deferred correction methods for the numerical solution of initial value problems in ordinary differential equations have recently been introduced by Dutt, Greengard and Rokhlin. A convergence proof is presented for these methods, based on the abstract Stetter-Lindberg-Skeel framework and Spijker-type norms. It is shown that p corrections of an order-r one-step solver yield order r(p+ 1) acc...
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ژورنال
عنوان ژورنال: Communications in Applied Mathematics and Computational Science
سال: 2009
ISSN: 2157-5452,1559-3940
DOI: 10.2140/camcos.2009.4.27