NDLI: Improvement of the Fitted Mesh Method by Three Transition Points Technique for Singularly Perturbed Problem with Two Parameters

Content Provider	IEEE Xplore Digital Library
Author	Xin Cai Da-xin Zhu Rui-qian Wu
Copyright Year	2009
Abstract	Singularly perturbed ordinary differential equation with two small parameters is considered. Firstly, the solution is decomposed into the smooth component and the singular component. The upper bounds of the smooth component and the singular component are studied. Secondly, the traditional Shishkin's scheme is presented and it is proved to be uniformly convergent with respect to the small parameter. Thirdly the technique of three transition points is introduced in order to improve the order of convergence . Three transition points scheme captures the property of boundary layer very well. It is a non equidistant method. It is proved to be uniformly convergent with respect to the small parameter in order one, which is higher than the traditional Shishkin's scheme. Finally, numerical results are given, which are in agreement with the theoretical results.
Starting Page	349
Ending Page	352
File Size	184835
Page Count	4
File Format	PDF
ISBN	9780769536347
DOI	10.1109/ICIC.2009.293
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2009-05-21
Publisher Place	UK
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Electrodes Upper bound numerical method Differential equations Elasticity singularly perturbed Mathematics Chemical reactors three transition points Convergence two small parameters
Content Type	Text
Resource Type	Article

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