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International Journal of Engineering Mathematics
Volume 2013 (2013), Article ID 482050, 9 pages
Research Article

Solution of Boundary Value Problems by Approaching Spline Techniques

Kakatiya Institute of Technology and Sciences, Warangal 506001, India

Received 23 March 2013; Revised 3 July 2013; Accepted 6 August 2013

Academic Editor: Shuli Sun

Copyright © 2013 P. Kalyani and P. S. Rama Chandra Rao. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


In the present work a nonpolynomial spline function is used to approximate the solution of the second order two point boundary value problems. The classes of numerical methods of second order, for a specific choice of parameters involved in nonpolynomial spline, have been developed. Numerical examples are presented to illustrate the applications of this method. The solutions of these examples are found at the nodal points with various step sizes and with various parameters (α, β). The absolute errors in each example are estimated, and the comparison of approximate values, exact values, and absolute errors of at the nodal points are shown graphically. Further, shown that nonpolynomial spline produces accurate results in comparison with the results obtained by the B-spline method and finite difference method.