Communications in Mathematical Sciences

Semi-implicit spectral deferred correction methods for ordinary differential equations

Michael L. Minion

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Abstract

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.

Article information

Source
Commun. Math. Sci., Volume 1, Number 3 (2003), 471-500.

Dates
First available in Project Euclid: 21 August 2009

Permanent link to this document
https://projecteuclid.org/euclid.cms/1250880097

Mathematical Reviews number (MathSciNet)
MR2069941

Zentralblatt MATH identifier
1088.65556

Keywords
Stiff equations fractional step methods method of lines

Citation

Minion, Michael L. Semi-implicit spectral deferred correction methods for ordinary differential equations. Commun. Math. Sci. 1 (2003), no. 3, 471--500. https://projecteuclid.org/euclid.cms/1250880097


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