Quintic spline solutions of boundary value problems

✍ Scribed by R.A. Usmani; S.A. Warsi

• Publisher: Elsevier Science
• Year: 1980
• Tongue: English
• Weight: 422 KB
• Volume: 6
• Category: Article
• ISSN: 0898-1221
• DOI: 10.1016/0898-1221(80)90028-0

✦ Synopsis

A new fourth order method using quintic polynomials is designed in this paper for the smooth approximation of the two point boundary value problems involving second order differential equations lacking the first derivative. The present method enables us to approximate the unknown function as well as its derivative at every point of the range of integration and thus it has obvious advantages over other discrete numerical methods. Our present method outperforms the well-known fourth order Noumerov's finite difference scheme. The convergence of the method is briefly outlined using matrix algebra and two numerical illustrations are provided to demonstrate the practical suitability of our approach. I. DEFINITION OF THE PROBLEM We consider the two point boundary value problem Y"(X) = W)Y(X) + g(x), Y(U) -A, = y(b) -Az = 0 (1.1)