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Title: Semi-implicit spectral deferred correction methods for ordinary differential equations

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 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 more efficient than semi-implicit Runge-Kutta methods for moderately stiff problems in terms of accuracy per function evaluation.

Authors:
Publication Date:
Research Org.:
Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
Sponsoring Org.:
USDOE Director, Office of Science. Office of Advanced Scientific Computing Research. Mathematical, Information, and Computational Sciences Division; National Science Foundation (US)
OSTI Identifier:
834319
Report Number(s):
LBNL-51096
R&D Project: KS1120; TRN: US200432%%238
DOE Contract Number:  
AC03-76SF00098
Resource Type:
Journal Article
Journal Name:
Communications in Mathematical Science
Additional Journal Information:
Journal Volume: 1; Journal Issue: 3; Other Information: Journal Publication Date: 2003; PBD: 6 Oct 2002
Country of Publication:
United States
Language:
English
Subject:
99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; ACCURACY; DIFFERENTIAL EQUATIONS; EVALUATION; MODIFICATIONS; PARTIAL DIFFERENTIAL EQUATIONS; RUNGE-KUTTA METHOD; STABILITY; METHOD OF LINES FRACTIONAL STEP METHODS STIFF EQUATIONS

Citation Formats

Minion, Michael L. Semi-implicit spectral deferred correction methods for ordinary differential equations. United States: N. p., 2002. Web.
Minion, Michael L. Semi-implicit spectral deferred correction methods for ordinary differential equations. United States.
Minion, Michael L. Sun . "Semi-implicit spectral deferred correction methods for ordinary differential equations". United States. https://www.osti.gov/servlets/purl/834319.
@article{osti_834319,
title = {Semi-implicit spectral deferred correction methods for ordinary differential equations},
author = {Minion, Michael L},
abstractNote = {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 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 more efficient than semi-implicit Runge-Kutta methods for moderately stiff problems in terms of accuracy per function evaluation.},
doi = {},
url = {https://www.osti.gov/biblio/834319}, journal = {Communications in Mathematical Science},
number = 3,
volume = 1,
place = {United States},
year = {2002},
month = {10}
}