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 Vladikavkaz. Mat. Zh., 2017, Volume 19, Number 4, Pages 50–57 (Mi vmj632)

A numerical method for the solution of fifth order boundary value problem in ordinary differential equations

P. K. Pandey

Dyal Singh College (University of Delhi), Lodhi Road, New Delhi-110003, India

Abstract: In this article we have proposed a technique for solving the fifth order boundary value problem as a coupled pair of boundary value problems. We have considered fifth order boundary value problem in ordinary differential equation for the development of the numerical technique. There are many techniques for the numerical solution of the problem considered in this article. Thus we considered the application of the finite difference method for the numerical solution of the problem. In this article we transformed fifth order differential problem into system of differential equations of lower order namely one and four. We discretized the system of differential equations into considered domain of the problem. Thus we got a system of algebraic equations. For the numerical solution of the problem, we have the system of algebraic equations. The solution of the algebraic equations is an approximate solution of the problem considered. Moreover we get numerical approximation of first and second derivative as a byproduct of the proposed method. We have shown that proposed method is convergent and order of accuracy of the proposed method is at lease quadratic. The numerical results obtained in computational experiment on the test problems approve the efficiency and accuracy of the method.

Key words: boundary value problem, cubic order convergence, difference method, fifth order differential equation, odd order problems, odd-even order problems.

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MSC: 65L10, 65L12
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Citation: P. K. Pandey, “A numerical method for the solution of fifth order boundary value problem in ordinary differential equations”, Vladikavkaz. Mat. Zh., 19:4 (2017), 50–57

Citation in format AMSBIB
\Bibitem{Pan17} \by P.~K.~Pandey \paper A numerical method for the solution of fifth order boundary value problem in ordinary differential equations \jour Vladikavkaz. Mat. Zh. \yr 2017 \vol 19 \issue 4 \pages 50--57 \mathnet{http://mi.mathnet.ru/vmj632} 

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This publication is cited in the following articles:
1. X. Dong, Zh. Liu, Sh. Li, “Similar constructing method for solving nonhomogeneous mixed boundary value problem of n-interval composite ode and its application”, Math. Meth. Appl. Sci., 42:5 (2019), 1702–1723
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