International Journal of Mathematical Sciences and Computing(IJMSC)
ISSN: 2310-9025 (Print), ISSN: 2310-9033 (Online)
Published By: MECS Press
IJMSC Vol.5, No.3, Jul. 2019
A Numerical Approach for Solving High-Order Boundary Value Problems
Full Text (PDF, 816KB), PP.1-16
In this paper, a numerical method which produces an approximate solution is presented for the numerical solutions of sixth,eighth,ninth and twelfth order boundary value problems. With the aid of derivatives of power series which slightly perturbe and collocate, eventually converts boundary value problems into the square matrix equations with the unknown coefficients obtain using MAPLE 18 software. This method gives the approximate solutions and compare with the exact solutions. Finally, some examples and their numerical solutions are given by comparing the numerical results obtained to other methods available in the literature, show a good agreement and efficiency.
Cite This Paper
Falade, K.I,"A Numerical Approach for Solving High-Order Boundary Value Problems", International Journal of Mathematical Sciences and Computing(IJMSC), Vol.5, No.3, pp. 1-16, 2019. DOI: 10.5815/ijmsc.2019.03.01
Agrawal R. Boundary value problems for higher ordinary differential equations. World Scientific,
Karageoghis .A, Philips T.N and Davies A.R, Spectral collocation methods for the Primary two-point boundary-value problems in modeling viscoelastic flows, International Journal for Numerical Methods in Engineering 26, 805-813, 1998.
Khan, M.S Finite-difference solutions of fifth-order boundary value problems, Ph.D thesis, Brunel University, England, 1994.
Wazwaz A.M, The numerical solution of fifth-order boundary value problems by the decomposition method, Journal of Computational and Applied Mathematics 136, 259–270, 2001.
Noor, M.A, Mohyud-Din,S.T,An efficient algorithm for solving fifth-order boundary value problems, Mathematical and computer modelling 45, 954–964, 2007.
Mohamed El-Gamel, Chebychev Polynomial Solutions of Twelfth-order Boundary-value Problems British Journal of Mathematics & Computer Science6 (1): Page19, Article no.BJMCS.2015.057, 2015
Abiodun A. O, Hilary I. O,Sunday O. E, Olasunmbo O. Agboola Differential Transform Technique for Higher Order Boundary Value Problems Modern Applied Science; Vol. 9, No.13.ISSN 1913-1844E-ISSN 1913-1852 Published by Canadian Center of Science and Education, 2015
Kasi Viswanadham K.N.S, Sreenivasulu Ballem Numerical Solution of Eighth Order Boundary Value Problems by Galerkin Method with Quintic B-splines International Journal of Computer Applications Volume 89 – No 15. Page 11, 2014
Muhammad S, Sirajul H, Safyan M,Imad Khan, Numerical solution of sixth-order boundary-value problems using Legendre wavelet collocation method. Published by Elsevier B.V. www.journals.elsevier.com/results-in-physics Page 1207, 2018
Falade K.I Exponentially fitted collocation approximation method for singular initial value problems and integro-differential equations. Ph.D Thesis (unpublished), University of Ilorin, Ilorin Nigeria, 2015 pp1-23
Falade K.I Numerical Solution of Higher Order Singular Initial Value Problems (SIVP) by Exponentially Fitted Collocation Approximate Method American International Journal of Research in Science, Technology, Engineering & Mathematics, 21(1), pp. 48-55 December 2017-February 2018.
Taiwo O. A. and Olagunju, A. S Chebyshev methods for the numerical solution of 4th order differential equations. Pioneer Journal of Mathematics and Mathematical Science, Vol 3(1). pp73. 2011.