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Author Liniger, W.
Source ACM Digital Library
Content type Text
Publisher Association for Computing Machinery (ACM)
File Format PDF
Language English
Subject Keyword Stopping criterion ♦ Ordinary differential equations ♦ Newton-raphson method ♦ Linear multistep formulas
Abstract In the numerical solution of ordinary differential equations, certain implicit linear multistep formulas, i.e. formulas of type ∑kj=0 αjxn+j - h ∑kj=0 βjxn+j = 0, (1) with βk> ≠ 0, have long been favored because they exhibit strong (fixed-h) stability. Lately, it has been observed [1-3] that some special methods of this type are unconditionally fixed-h stable with respect to the step size. This property is of great importance for the efficient solution of stiff [4] systems of differential equations, i.e. systems with widely separated time constants. Such special methods make it possible to integrate stiff systems using a step size which is large relative to the rate of change of the fast-varying components of the solution.
Description Affiliation: IBM Thomas J. Watson Research Center, Yorktown Heights, NY (Liniger, W.)
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 14
Issue Number 9
Page Count 2
Starting Page 600
Ending Page 601

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Source: ACM Digital Library