IJMMS International Journal of Mathematics and Mathematical Sciences 1687-0425 0161-1712 Hindawi Publishing Corporation 518247 10.1155/S0161171280000099 Spline solutions for nonlinear two point boundary value problems Usmani Riaz A. Department of Applied Mathematics The University of Manitoba Winnipeg Manitoba R3T 2N2 Canada umanitoba.ca 1980 3 1 151 167 27 04 1979 1980 Copyright © 1980 Hindawi Publishing Corporation

Necessary formulas are developed for obtaining cubic, quartic, quintic, and sextic spline solutions of nonlinear boundary value problems. These methods enable us to approximate the solution of the boundary value problems, as well as their successive derivatives smoothly. Numerical evidence is included to demonstrate the relative performance of these four techniques.

 cubic quartic quintic and sextic spline functions; finite difference scheme; Noumerov's formula; Newton's method for solving nonlinear algebraic equations; nonlinear two point boundary value problem; recurrence relations