Accession Number : ADA337779
Title : Spectral Deferred Correction Methods for Ordinary Differential Equations
Descriptive Note : Research rept.
Corporate Author : YALE UNIV NEW HAVEN CT DEPT OF COMPUTER SCIENCE
Personal Author(s) : Dutt, Alok ; Greengard, Leslie ; Rokhlin, Vladimir
PDF Url : ADA337779
Report Date : 30 JAN 1998
Pagination or Media Count : 29
Abstract : We introduce a new class of methods for the Cauchy problem for ordinary differential equations (ODEs). We begin by converting the original ODE into the corresponding Picard equation and apply a deferred correction procedure in the integral formulation, driven by either the explicit or the implicit Euler marching scheme. The approach results in algorithms of essentially arbitrary order accuracy for both non-stiff and stiff problems; their performance is illustrated with several numerical examples. For non-stiff problems, the stability behavior of the obtained explicit schemes is very satisfactory and algorithms with orders between 8 and 20 should be competitive with the best existing ones. In our preliminary experiments with stiff problems, a simple adaptive implementation of the method demonstrates performance comparable to that of a state-of-the-art extrapolation code (at least, at moderate to high precision). Deferred correction approach based on the Picard equation appears to be a promising candidate for further investigation.
Descriptors : *PARTIAL DIFFERENTIAL EQUATIONS, *CAUCHY PROBLEM, ALGORITHMS, APPROXIMATION(MATHEMATICS), NUMERICAL INTEGRATION, INTERPOLATION, INTEGRAL EQUATIONS, ERROR CORRECTION CODES, EXTRAPOLATION.
Subject Categories : Numerical Mathematics
Distribution Statement : APPROVED FOR PUBLIC RELEASE