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Author Liniger, Werner
Source ACM Digital Library
Content type Text
Publisher Association for Computing Machinery (ACM)
File Format PDF
Language English
Subject Keyword Strict stability ♦ Stiff equations ♦ A0-stability ♦ Parametrized linear multistep formulas ♦ A∞-stability ♦ Order of accuracy
Abstract This paper is concerned with stability and accuracy of families of linear k-step formulas depending on parameters, with particular emphasis on the numerical solution of stiff ordinary differential equations. An upper bound, p = k, is derived for the order of accuracy of A∞-stable formulas. Three criteria are given for A0-stability. It is shown that (1) for p = k, k arbitrary, A∞-stability implies certain necessary conditions for A0-stability and for strict stability (meaning that the extraneous roots of &rgr;(&zgr;) satisfy |&zgr;| < 1); (2) for p = k = 2, 3, 4, and 5, A∞-stability (for k = 5 together with another constraint) implies strict stability; and (3) for certain one-parameter classes of formulas with p = k = 3, 4, and/or 5, A∞-stability implies A0-stability.
Description Affiliation: IBM Thomas J. Watson Research Center, Yorktown Heights, NY (Liniger, Werner)
Age Range 18 to 22 years ♦ above 22 year
Educational Use Research
Education Level UG and PG
Learning Resource Type Article
Publisher Date 2005-08-01
Publisher Place New York
Journal Communications of the ACM (CACM)
Volume Number 18
Issue Number 1
Page Count 4
Starting Page 53
Ending Page 56


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Source: ACM Digital Library