### Boundary Value Techniques for the Numerical Solution of Certain Initial Value Problems in Ordinary Differential EquationsBoundary Value Techniques for the Numerical Solution of Certain Initial Value Problems in Ordinary Differential Equations

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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