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Abstract and Applied Analysis
Volume 2014 (2014), Article ID 794716, 6 pages
http://dx.doi.org/10.1155/2014/794716
Research Article

Solving Singularly Perturbed Multipantograph Delay Equations Based on the Reproducing Kernel Method

Department of Mathematics, Changshu Institute of Technology, Changshu, Jiangsu 215500, China

Received 13 November 2013; Accepted 20 January 2014; Published 27 February 2014

Academic Editor: Valery Y. Glizer

Copyright © 2014 F. Z. Geng and S. P. Qian. 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

A numerical method is presented for solving the singularly perturbed multipantograph delay equations with a boundary layer at one end point. The original problem is reduced to boundary layer and regular domain problems. The regular domain problem is solved by combining the asymptotic expansion and the reproducing kernel method (RKM). The boundary layer problem is treated by the method of scaling and the RKM. Two numerical examples are provided to illustrate the effectiveness of the present method. The results from the numerical example show that the present method can provide very accurate analytical approximate solutions.