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Journal of Advances in Mathematics and Computer Science, ISSN: 2456-9968, ISSN: 2231-0851 (Past),Vol.: 27, Issue.: 1

Original-research-article

Cubic B-Spline Collocation and Adomian Decomposition Methods on 4th Order Multi-point Boundary Value Problems

 

E. U. Agom1*, F. O. Ogunfiditimi2, B. E. A. Eno1 and I. M Esuabana1
1Department of Mathematics, University of Calabar, Calabar, Nigeria.
2Department of Mathematics, University of Abuja, Abuja, Nigeria.

Article Information
Editor(s):
(1) Octav Olteanu, Professor, Department of Mathematics-Informatics, University Politehnica of Bucharest, Bucharest, Romania.
Reviewers:
(1) A. A. Opanuga, Covenant University, Nigeria.
(2) Zehra Pinar, Namk Kemal University, Turkey.
(3) Chaouchi Belkacem, Khemis Miliana University, Algeria.
Complete Peer review History: http://sciencedomain.org/review-history/24162

Abstracts

In this paper, Cubic B-Spline collocation method (CBSCM) and Adomian Decomposition Method (ADM) are applied to obtain numerical solutions to fourth-order linear and nonlinear differential equations. The CBSCM was based on finite element method involving collocation method with cubic B-spline as a basis function. While ADM was based on multistage decomposition method. We discovered in the illustrative examples considered, that result by ADM were compatible with the closed form solutions well over twenty, in some cases over thirty, decimal places and with extremely minimal absolute errors. Results by CBSCM gave correct solutions to atmost six decimal places with sizeable absolute errors. These has further revealed the importance and superiority of ADM over CBSCM in providing semi-analytic solution to this class of differential equations.

Keywords :

Cubic b-spline; Adomian decomposition method; boundary value problems; 4th order differential equations.

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DOI : 10.9734/JAMCS/2018/40656

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