An iterative numerical method for singularly perturbed reaction-diffusion equations with negative shift

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• 作者：P. Avudai Selvi ^{avudaiselvi12@gmail.com" class="auth_mail" title="E-mail the corresponding author} ; N. Ramanujam ; ^{matram2k3@gmail.com" class="auth_mail" title="E-mail the corresponding author}
• 关键词：34K10 ; 34K26 ; 34K28
• 刊名：Journal of Computational and Applied Mathematics
• 出版年：2016
• 出版时间：April 2016
• 年：2016
• 卷：296
• 期：Complete
• 页码：10-23
• 全文大小：427 K

文摘

In this paper, a numerical method based on an iterative scheme is proposed for a singularly perturbed delay differential equation of reaction–diffusion type. In this method the solution of the delay problem is obtained as the limit of the solutions to a sequence of the non-delay problems. The numerical solutions of the non-delay problems are obtained by applying existing finite difference schemes and finite element method for the non-delay singularly perturbed equations. Error estimates are derived in the supremum norm. Numerical results illustrating the theory are also included.