Solution of Second Order Linear and Nonlinear Two Point Boundary Value Problems Using Legendre Operational Matrix of Differentiation

Abdurkadir Edeo


In this paper, an approach using Tau method based on Legendre operational matrix of differentiation [2] & [5] has been addressed to find the solutions of second order linear and nonlinear two point boundary value problems of ordinary differential equations. In the implementation of this approach, the given second order two point boundary problems is converted into a system of algebraic equations, whose solutions are the Legendre coefficients. The validity and efficiency of the method has also been illustrated with numerical examples supported by graphs.


Boundary Value Problems (BVPs); Legendre Operational Matrix of Differentiation; Linear and nonlinear ordinary differential equations.

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J. Douglas Faires & Richard L.Burden.“Numerical Methods.” Brooks Cole, Third Edition, June 18, 2002.

Chahn Yong Jung, Zeqing Liu, Arif Rafiq, Faisal Ali,& Shin Min Kang. “Solution of Second Order Linear and Nonlinear Ordinary Differential Equations Using Legendre Operational Matrix of Differentiation.” International Journal of Pure and Applied Mathematics. Volume 93 No. 2 2014.

Md. Shafiqul Islam, Afroza Shirin.“Numerical Solutions of a Class of Second Order Boundary Value Problems on Using Bernoulli Polynomials.” Applied Mathematics, 2, pp.1059-1067,2011.

Yogesh Gupta.“A Numerical Algorithm for Solution of Boundary Value Problems with Applications.” International Journal of Computer Applications. Volume 40, No.8, February 2012.

Abbas Saadatmandi, Mehdi Dehghan. “A New Operational Matrix for Solving Fractional-Order Differential Equations.” Computers and Mathematics with Applications 59, pp. 1326-1336, 2010.

Nur Nadiah Abd Hamid, Ahmad Abd. Majid & Ahmad Izani Md. Ismail. “Extended Cubic B-Spline Method for Linear Two-Point Boundary Value Problems.” Sains Malaysiana 40(11), pp.1285–1290, 2011.

J. Rashidinia and Sh. Sharif. “B-Spline Method for Two-Point Boundary Value Problems.” International Journal of Mathematical Modelling & Computations. Vol. 05, No. 02, pp. 111- 125, Spring 2015.

M. M. Rahman, M.A. Hossen, M. Nurul Islam and Md. Shajib Ali. “Numerical Solutions of Second Order Boundary Value Problems by Galerkin Method with Hermite Polynomials.” Annals of Pure and Applied Mathematics. Vol. 1, No. 2, pp.138-148, 2012.

Li-Bin Liu, Huan-Wen Liu, Yanping Chen. “Polynomial spline approach for solving second-order boundary-value problems with Neumann conditions.” Applied Mathematics and Computation 217, pp.6872–6882, 2011.


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