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Author Usmani, Riaz A.
Source ACM Digital Library
Content type Text
Publisher Association for Computing Machinery (ACM)
File Format PDF
Copyright Year ©1966
Language English
Subject Domain (in DDC) Computer science, information & general works ♦ Data processing & computer science
Abstract Linear initial value problems, particularly involving first order differential equations, can be transformed into systems of higher order and treated as boundary value problems. The type of difference equations used to replace the associated second order boundary value problem are $\textit{yn}$ - $2\textit{y}\textit{n}+1$ + $\textit{y}\textit{n}+2$ = $\textit{h}2$ ∑ $\textit{βiy″}\textit{n}+\textit{i}$ + $\textit{h}3;$ ∑ $\textit{δi}\textit{y}‴\textit{n}+\textit{i}$ + · · ·, $\textit{n}$ = 1, 2, · · ·, $\textit{N}$ - 1 and - $\textit{yN}$ + $\textit{y}\textit{N}+1$ = $\textit{h}(\textit{b}0\textit{y′}\textit{N}$ + $\textit{b}1\textit{y′}\textit{N}+1)$ + $\textit{h}2;(\textit{c}0\textit{y″}\textit{N}$ + $\textit{c}1\textit{y″}\textit{N}+1)$ + · · ·.Numerical techniques referred to as $\textit{M}1,$ $\textit{M}2,$ and $\textit{M}3$ have been developed in which error is $\textit{O}(\textit{h}4),$ $\textit{O}(\textit{h}6)$ and $\textit{O}(\textit{h}8),$ respectively. Experimental results have been given to demonstrate the usefulness of method $\textit{M}3$ over $\textit{M}1$ or $\textit{M}2.$
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 1966-04-01
Publisher Place New York
e-ISSN 1557735X
Journal Journal of the ACM (JACM)
Volume Number 13
Issue Number 2
Page Count 9
Starting Page 287
Ending Page 295

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Source: ACM Digital Library