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W. Auzinger, H. Hofstätter, W. Kreuzer, E. Weinmüller:
"Defect correction as a family of iterative techniques for ODEs";
Talk: SciCADE 2003, Trondheim; 2003-06-30 - 2003-07-04.

Since its introduction in the 1970's, the idea of iterated defect correction (IDeC) has been successfully applied to various classes of differential equations. The classical IDeC method uses an interpolant of a given, basic discrete approximation, from which the defect with respect to the given ODE is computed. This defect is used to define an auxiliary, neighboring problem whose exact solution is known. Solving the neighboring problem with the basic discretization scheme yields a global error estimate. This can be used to construct an improved approximation, and the procedure can be iterated. The fixed point of such an iterative process corresponds to a certain collocating solution.

We present a variety of modifications to this algorithm. Some of these have been proposed only recently, and together they form a family of iterative techniques, each with its particular advantages. These modifications are based on techniques like defect interpolation (IPDeC), defect quadrature (IQDeC), and combinations thereof. We investigate the convergence on (locally) equidistant and nonequidistant grids, including special choices like Gaussian nodes.

http://publik.tuwien.ac.at/files/pub-tm_948.pdf