Quartic Nonpolynomial Spline Solutions for Third Order Two-Point Boundary Value Problem

Authors: Talaat S. El-Danaf

Abstract:

In this paper, we develop quartic nonpolynomial spline method for the numerical solution of third order two point boundary value problems. It is shown that the new method gives approximations, which are better than those produced by other spline methods. Convergence analysis of the method is discussed through standard procedures. Two numerical examples are given to illustrate the applicability and efficiency of the novel method.

Keywords: Quartic nonpolynomial spline, Two-point boundary value problem.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1081769

References:

[1] E.A. Al-Said, M.A. Noor, "Cubic Splines Method for a System of Third Boundary Value Problems", Applied Mathematics and Computations 142 (2003) 195-204.
[2] H.N.Calagar, S.H.Cagalar and E.H.Twizell, "The Numerical Solution of Third Order Boundary Value Problems with Fourth Degree B-Spline", International Journal of Computer Mathematics 71(1999) 373-381.
[3] A. Khan and T. Aziz, "The Numerical Solution of Third Order Boundary Value Problems using quintic spline", Applied Mathematics and Computations137 (2003) 253-260.
[4] M.A. Noor, E.A. Al-Said, "Quartic Spline Solutions of Third Order Obstacle Boundary Value Problems", Applied Mathematics and Computations, 153(2004) 307-316.
[5] M.A. Ramadan, I.F.Lashien and W.K.Zahra, "Polynomial and Nonpolynomial Spline Approaches to the Numerical Solution of Second Order Boundary Value Problems", Applied Mathematics and Computations 184(2007) 476-484.
[6] M. A. Ramadan, T. S. El-Danaf and Faisal E. I. Abd-Alaal, "Application of the Non-Polynomial Spline Approach to the Solution of the Burgers- equation", The Open Applied Mathematics Journal, Vol. 1, (2007) 15 - 20.
[7] T. S. El-Danaf and Faisal E. I. Abd-Alaa1, "The use of non-polynomial splines for solving a fourth - order parabolic partial differential equation", Proceeding of the Mathematical and Physical Society of Egypt, accepted.