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Mathematical Problems in Engineering
Volume 2015, Article ID 561489, 6 pages
http://dx.doi.org/10.1155/2015/561489
Research Article

Block Hybrid Collocation Method with Application to Fourth Order Differential Equations

1Department of Mathematical and Actuarial Sciences, Universiti Tunku Abdul Rahman, Setapak, 53300 Kuala Lumpur, Malaysia
2Department of Mathematics and Institute for Mathematical Research, Universiti Putra Malaysia (UPM), 43400 Serdang, Selangor, Malaysia

Received 10 July 2014; Revised 22 November 2014; Accepted 25 November 2014

Academic Editor: María Isabel Herreros

Copyright © 2015 Lee Ken Yap and Fudziah Ismail. 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.

Abstract

The block hybrid collocation method with three off-step points is proposed for the direct solution of fourth order ordinary differential equations. The interpolation and collocation techniques are applied on basic polynomial to generate the main and additional methods. These methods are implemented in block form to obtain the approximation at seven points simultaneously. Numerical experiments are conducted to illustrate the efficiency of the method. The method is also applied to solve the fourth order problem from ship dynamics.