British Journal of Mathematics & Computer Science, ISSN: 2231-0851,Vol.: 3, Issue.: 2 (April-June)

## Original-research-article

Solution of a Linear Third order Multi-Point Boundary Value Problem using RKM

Ghazala Akram1*, Muhammad Tehseen1, Shahid S. Siddiqi1 and Hamood ur Rehman1

1Department of Mathematics, University of the Punjab,Lahore, Pakistan.

Article Information

Editor(s):

(1) Dragoş - Pătru Covei, Department of Mathematics, University “Constantin Brâncuşi” of Târgu-Jiu, România.

(2) Narayan Thapa, Department of Mathematics and Computer Science, Minot State University, Minot, USA.

Reviewers:

(1) Anonymous.

(2) Anonymous.

(3) Anonymous.

Complete Peer review History: http://www.sciencedomain.org/review-history/1169

Abstracts

Aims: In this paper an approximate method for the solution of third-order differential equation with two and three point boundary condition is developed using iterative reproducing kernel method.
Methods: The third order boundary value problem is converted into integro-differential equation of second order two point boundary value problem.
The reproducing kernel method which takes the form of a convergent series with easily computable components is used for the solution of second order two point boundary value problem.
Results: Six numerical examples are given to demonstrate the efficiency of the present method. The results obtained are better than the existing methods developed in [19,20,21,22,23].
Conclusions: In this paper, the solution of linear and nonlinear third order (two and three point) boundary value problem is determined. For the solution of third order three point boundary value problem reproducing kernel method is proposed and obtained a good accuracy in absolute errors. As the reproducing kernel method cannot solve the third order three-point boundary value problems directly, so the third order boundary value problem is converted to second order two point boundary value problem after absorbing the nonlocal condition at . The method developed is compared with those developed by Li et al. , El-Salam et al. , Khan and Aziz , Li and Wu  and Wu and Li . As observed in Example 3, 4, 5 and 6 that the method obtained in this paper is better than -. Results obtained using the scheme presented here show that the numerical scheme is very effective and convenient for third-order linear as well as nonlinear boundary value problem.

Keywords :

Approximate solution, gram-Schmidt orthogonal process, reproducing kernel space, integro-differential equation, nonlinear.

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