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## Archive of Issues

India New Delhi
Year
2019
Volume
29
Issue
3
Pages
341-350
 Section Mathematics Title The numerical solution of a nonlocal boundary value problem for an ordinary second-order differential equation by the finite difference method Author(-s) Pandey P.K.a Affiliations University of Delhi, Dyal Singh Collegea Abstract In the article a numerical technique based on the finite difference method is proposed for the approximate solution of a second order nonlocal boundary value problem for ordinary differential equations. It is clear that a bridge designed with two support points at each end point leads to a standard two-point local boundary value condition, and a bridge contrived with multi-point supports corresponds to a multi-point boundary value condition. At the same time if non-local boundary conditions can be set up near each endpoint of a multi-point support bridge, a two-point nonlocal boundary condition arises. The computational results for the nonlinear model problem are presented to validate the proposed idea. The effect of parameters variation on the convergence of the proposed method is analyzed. Keywords second-order boundary value problem, finite difference method, integral boundary conditions, parameters and convergence UDC 519.624 MSC 65L10, 65L12 DOI 10.20537/vm190305 Received 11 May 2019 Language English Citation Pandey P.K. The numerical solution of a nonlocal boundary value problem for an ordinary second-order differential equation by the finite difference method, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2019, vol. 29, issue 3, pp. 341-350. References Zou Y., Hu Q., Zhang R. On numerical studies of multi-point boundary value problem and its fold bifurcation, Applied Mathematics and Computation, 2007, vol. 185, issue 1, pp. 527-537. https://doi.org/10.1016/j.amc.2006.07.064 Cannon J.R. The solution of the heat equation subject to the specification of energy, Quarterly of Applied Mathematics, 1963, vol. 21, no. 2, pp. 155-160. https://www.jstor.org/stable/43635292 Ionkin N.I. The solution of a certain boundary value problem of the theory of heat conduction with a nonclassical boundary condition, Differentsial'nye Uravneniya, 1977, vol. 13, no. 2, pp. 294-304 (in Russian). http://mi.mathnet.ru/eng/de2993 Chegis R.Y. Numerical solution of the heat conduction problem with an integral condition, Litovskii Matematicheskii Sbornik, 1984, vol. 24, no. 4, pp. 209-215 (in Russian). Khan R.A. The generalized method of quasilinearization and nonlinear boundary value problems with integral boundary conditions, Electronic Journal of Qualitative Theory of Differential Equations, 2003, no. 19, pp. 1-15. https://doi.org/10.14232/ejqtde.2003.1.19 Feng M., Ji D., Ge W. Positive solutions for a class of boundary value problem with integral boundary conditions in Banach spaces, Journal of Computational and Applied Mathematics, 2008, vol. 222, issue 2, pp. 351-363. https://doi.org/10.1016/j.cam.2007.11.003 Boucherif A. Second-order boundary value problems with integral boundary conditions, Nonlinear Analysis: Theory, Methods & Applications, 2009, vol. 70, issue 1, pp. 364-371. https://doi.org/10.1016/j.na.2007.12.007 Liu L., Hao X., Wu Y. Positive solutions for singular second order differential equations with integral boundary conditions, Mathematical and Computer Modelling, 2013, vol. 57, issues 3-4, pp. 836-847. https://doi.org/10.1016/j.mcm.2012.09.012 Gupta C.P. A generalized multi-point boundary value problem for second order ordinary differential equations, Applied Mathematics and Computation, 1998, vol. 89, issues 1-3, pp. 133-146. https://doi.org/10.1016/S0096-3003(97)81653-0 Guo Y., Shan W., Ge W. Positive solutions for second-order m-point boundary value problems, Journal of Computational and Applied Mathematics, 2003, vol. 151, issue 2, pp. 415-424. https://doi.org/10.1016/S0377-0427(02)00739-2 Kong L., Kong Q. Multi-point boundary value problems of second-order differential equations (I), Nonlinear Analysis: Theory, Methods & Applications, 2004, vol. 58, issues 7-8, pp. 909-931. https://doi.org/10.1016/j.na.2004.03.033 Ma R. Positive solutions for nonhomogeneous $m$-point boundary value problems, Computers & Mathematics with Applications, 2004, vol. 47, issues 4-5, pp. 689-698. https://doi.org/10.1016/S0898-1221(04)90056-9 Pandey P.K. A finite difference method for the numerical solving general third order boundary-value problem with an internal boundary condition, Russian Mathematics, 2017, vol. 61, issue 12, pp. 29-38. https://doi.org/10.3103/S1066369X17120040 Froberg C.E. Introduction to numerical analysis, 2nd ed., New York: Addison-Wesley, 1969. Jain M.K., Iyenger S.R.K., Jain R.K. Numerical methods for scientific and engineering computation (2/e), New Delhi: Wiley Eastern Limited, 1987. Full text