tailieunhanh - Báo cáo hóa học: " Research Article A Parameter Robust Method for Singularly Perturbed Delay Differential Equations Fevzi Erdogan"

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 A Parameter Robust Method for Singularly Perturbed Delay Differential Equations Fevzi Erdogan | Hindawi Publishing Corporation Journal of Inequalities and Applications Volume 2010 Article ID 325654 14 pages doi 2010 325654 Research Article A Parameter Robust 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@ Received 29 April 2010 Revised 9 July 2010 Accepted 17 July 2010 Academic Editor Alexander I. Domoshnitsky Copyright 2010 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. Uniform finite difference methods are constructed via nonstandard finite difference methods for the numerical solution of singularly perturbed quasilinear initial value problem for delay differential equations. A numerical method is constructed for this problem which involves the appropriate Bakhvalov meshes on each time subinterval. The method is shown to be uniformly convergent with respect to the perturbation parameter. A numerical example is solved using the presented method and the computed result is compared with exact solution of the problem. 1. Introduction Delay differential equations are used to model a large variety of practical phenomena in the biosciences engineering and control theory and in many other areas of science and technology in which the time evolution depends not only on present states but also on states at or near a given time in the past see . 1-4 . If we restrict the class of delay differential equations to a class in which the highest derivative is multiplied by a small parameter then it is said to be a singularly perturbed delay differential equation. Such problems arise in the mathematical modeling of various practical phenomena for example in population dynamics 4 the study of bistable devices