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Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article An Exponentially Fitted Method for Singularly Perturbed Delay Differential Equations Fevzi Erdogan | Hindawi Publishing Corporation Advances in Difference Equations Volume 2009 Article ID 781579 9 pages doi 10.1155 2009 781579 Research Article An Exponentially Fitted Method for Singularly Perturbed Delay Differential Equations Fevzi Erdogan Department of Mathematics Faculty of Sciences Yuzuncu Yil University 65080 Van Turkey Correspondence should be addressed to Fevzi Erdogan ferdogan@yyu.edu.tr Received 4 November 2008 Accepted 16 January 2009 Recommended by Istvan Gyori This paper deals with singularly perturbed initial value problem for linear first-order delay differential equation. An exponentially fitted difference scheme is constructed in an equidistant mesh which gives first-order uniform convergence in the discrete maximum norm. The difference scheme is shown to be uniformly convergent to the continuous solution with respect to the perturbation parameter. A numerical example is solved using the presented method and compared the computed result with exact solution of the problem. Copyright 2009 Fevzi Erdogan. 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. 1. Introduction Delay differential equations play an important role in the mathematical modelling of various practical phenomena in the biosciences and control theory. Any system involving a feedback control will almost always involve time delays. These arise because a finite time is required to sense information and then react to it. A singularly perturbed delay differential equation is an ordinary differential equation in which the highest derivative is multiplied by a small parameter and involving at least one delay term 1-4 . Such problems arise frequently in the mathematical modelling of various practical phenomena for example in the modelling of several physical and biological phenomena like the optically bistable devices 5 description of
