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Author Gragg, William B. ♦ Stetter, Hans J.
Source ACM Digital Library
Content type Text
Publisher Association for Computing Machinery (ACM)
File Format PDF
Copyright Year ©1964
Language English
Subject Domain (in DDC) Computer science, information & general works ♦ Data processing & computer science
Abstract The order $\textit{p}$ which is obtainable with a stable $\textit{k}-step$ method in the numerical solution of $\textit{y′}$ = $\textit{f}(\textit{x},$ $\textit{y})$ is limited to $\textit{p}$ = $\textit{k}$ + 1 by the theorems of Dahlquist. In the present paper the customary schemes are modified by including the value of the derivative at one “nonstep point;” as usual, this value is gained from an explicit predictor. It is shown that the order of these generalized predictor-corrector methods is not subject to the above restrictions; stable $\textit{k}-step$ schemes with $\textit{p}$ = $2\textit{k}$ + 2 have been constructed for $\textit{k}$ ≤ 4. Furthermore it is proved that methods of order $\textit{p}$ actually converge like $\textit{hp}$ uniformly in a given interval of integration. Numerical examples give some first evidence of the power of the new methods.
ISSN 00045411
Age Range 18 to 22 years ♦ above 22 year
Educational Use Research
Education Level UG and PG
Learning Resource Type Article
Publisher Date 1964-04-01
Publisher Place New York
e-ISSN 1557735X
Journal Journal of the ACM (JACM)
Volume Number 11
Issue Number 2
Page Count 22
Starting Page 188
Ending Page 209

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Source: ACM Digital Library