Cubic B-Spline Collocation and Adomian Decomposition Methods on 4th Order Multi-point Boundary Value Problems
E. U. Agom *
Department of Mathematics, University of Calabar, Calabar, Nigeria.
F. O. Ogunfiditimi
Department of Mathematics, University of Abuja, Abuja, Nigeria.
B. E. A. Eno
Department of Mathematics, University of Calabar, Calabar, Nigeria.
I. M Esuabana
Department of Mathematics, University of Calabar, Calabar, Nigeria.
*Author to whom correspondence should be addressed.
Abstract
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.