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Author Willers, I. M.
Source ACM Digital Library
Content type Text
Publisher Association for Computing Machinery (ACM)
File Format PDF
Language English
Subject Keyword Integration ♦ Singularities ♦ Program comparison ♦ Initial value problem ♦ Ordinary differential equations ♦ Taylor series ♦ Continued fractions
Abstract A new integration algorithm is found, and an implementation is compared with other programmed algorithms. The new algorithm is a step-by-step procedure for solving the initial value problem in ordinary differential equations. It is designed to approximate poles of small integer order in the solutions of the differential equations by continued fractions obtained by manipulating the sums of truncated Taylor series expansions.The new method is compared with the Gragg-Bulirsch-Stoer, and the Taylor series method. The Taylor series method and the new method are shown to be superior in speed and accuracy, while the new method is shown to be most superior when the solution is required near a singularity. The new method can finally be seen to pass automatically through singularities where all the other methods which are discussed will have failed.
Description Affiliation: CERN, Geneve, Switzerland (Willers, I. M.)
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 17
Issue Number 9
Page Count 5
Starting Page 504
Ending Page 508


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Source: ACM Digital Library