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مقالات فارسیISIکنفرانسهاژورنالها

A fourth-order optimal numerical approximation and its convergence for singularly perturbed time delayed parabolic problems

محل انتشار: مجله ایرانی آنالیز عددی و بهینه سازی، دوره: 12، شماره: 2
سال انتشار: 1401
نوع سند: مقاله ژورنالی
زبان: انگلیسی
مشاهده: 105

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لینک ثابت به این مقاله:
https://civilica.com/doc/1529660

شناسه ملی سند علمی:

JR_IJNAO-12-2_001

تاریخ نمایه سازی: 11 مهر 1401

چکیده مقاله:

This paper presents a numerical solution for a time delay parabolic problem (reaction-diffusion) containing a small parameter. The numerical method combines the implicit Crank–Nicolson scheme for the time  derivative on the uniform mesh and the central difference scheme for the spatial derivative on the Shishkin type meshes. It is shown to be second-order uniformly convergent in time and space. Then Richardson extrapolation technique is applied to enhance the accuracy from second-order to fourth-order. The error analysis is carried out, and the method is proved to be uniformly convergent. These two methods are applied to two test examples in support of the theoretical results. 

کلیدواژه ها:

Time delayed parabolic problem ، boundary layer ، Post processing technique ، Singular perturbation

نویسندگان

J. Mohapatra

Department of Mathematics, National Institute of Technology Rourkela, ۷۶۹۰۰۸, India,

L. Govindarao

Department of Mathematics, Amrita School of Engineering Coimbatore, Amrita Vishwa Vidyapeetham, Amrita University, Ettimadai, Tamilnadu, India,

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