IJPAM: Volume 43, No. 4 (2008)

A CUBIC SPLINE METHOD FOR SOLVING A SYSTEM
OF THIRD ORDER BOUNDARY VALUE PROBLEMS

Eisa A. Al-Said
Department of Mathematics
King Saud University
P.O. Box 2455, Riyadh, 11451, KINGDOM OF SAUDI ARABIA
e-mail: se992003@yahoo.com


Abstract.We use uniform cubic polynomial splines to develop a new numerical method for computing approximations to the solution and its first and second derivatives for a system of third order boundary value problems. Such a system arise in physical oceanography and can be studied in the framework of variational inequality theory. It is shown that the present method is of order two and gives approximations which are better than those produced by other collocation, finite difference and spline methods when solving such a system. Numerical example is presented to illustrate applicability of the new method.

Received: February 15, 2008

AMS Subject Classification: 65N30, 49J40

Key Words and Phrases: cubic spline, finite difference technique, third order boundary value problems, obstacle problems

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2008
Volume: 43
Issue: 4