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September 2003 Semi-implicit spectral deferred correction methods for ordinary differential equations
Michael L. Minion
Commun. Math. Sci. 1(3): 471-500 (September 2003).


A semi-implicit formulation of the method of spectral deferred corrections (SISDC) for ordinary differential equations with both stiff and non-stiff terms is presented. Several modifications and variations to the original spectral deferred corrections method by Dutt, Greengard, and Rokhlin concerning the choice of integration points and the form of the correction iteration are presented. The stability and accuracy of the resulting ODE methods for both stiff and nonstiff problems are explored analytically and numerically. The SISDC methods are intended to be combined with the method of lines approach to yield a flexible framework for creating higher-order semi-implicit methods for partial differential equations. A discussion and numerical examples of the SISDC method applied to advection-diffusion type equations are included. The results suggest that higher-order SISDC methods are a competitive alternative to existing Runge-Kutta and linear multistep methods based on the accuracy per function evaluation.


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Michael L. Minion. "Semi-implicit spectral deferred correction methods for ordinary differential equations." Commun. Math. Sci. 1 (3) 471 - 500, September 2003.


Published: September 2003
First available in Project Euclid: 21 August 2009

zbMATH: 1088.65556
MathSciNet: MR2069941

Keywords: fractional step methods , method of lines , Stiff equations

Rights: Copyright © 2003 International Press of Boston

Vol.1 • No. 3 • September 2003
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