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Journal of Applied Mathematics
Volume 2014 (2014), Article ID 348912, 10 pages
http://dx.doi.org/10.1155/2014/348912
Research Article

Solving Delay Differential Equations of Small and Vanishing Lag Using Multistep Block Method

1Institute for Mathematical Research, Universiti Putra Malaysia (UPM), 43400 Serdang, Selangor, Malaysia
2Mathematics Department, Faculty of Science, Universiti Putra Malaysia (UPM), 43400 Serdang, Selangor, Malaysia

Received 8 May 2014; Accepted 6 September 2014; Published 29 October 2014

Academic Editor: Ferenc Hartung

Copyright © 2014 Nurul Huda Abdul Aziz et al. 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

This paper considers the numerical solution of delay differential equations for solving the problem of small and vanishing lag using multistep block method. This problem arises when the size of a delay value is smaller than the step size, , and the delay time may even vanish when in a current step. The proposed approach that is based on interpolation of Newton divided difference has been implemented by adapting this problem to the multistep block method. In order to achieve the required accuracy, this approach considered the appropriate degree of interpolation polynomial in approximating the solution of delay term. The developed code for solving small and vanishing lag is done using C program and we called it as DDEB5. The P-stability and Q-stability of this method are also studied. Numerical results are presented and compared to the existing method in order to illustrate the efficiency of the proposed method.