کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4631175 1340617 2011 12 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
A novel fitted operator finite difference method for a singularly perturbed delay parabolic partial differential equation
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات کاربردی
پیش نمایش صفحه اول مقاله
A novel fitted operator finite difference method for a singularly perturbed delay parabolic partial differential equation
چکیده انگلیسی

We design a robust fitted operator finite difference method for the numerical solution of a singularly perturbed delay parabolic partial differential equation. This method is unconditionally stable and is convergent with order O(k+h2)O(k+h2), where k and h   are respectively the time and space step-sizes, which is better than the one obtained by Ansari et al. [A.R. Ansari, S.A. Bakr, G.I. Shishkin, A parameter-robust finite difference method for singularly perturbed delay parabolic partial differential equations, J. Comput. Appl. Math. 205 (2007) 552–566] where they have used a fitted mesh finite difference method. Their method was of the order ONt-1+Nx-2ln2Nx, where Nt and Nx denote the total number of sub-intervals in the time and space directions. The performance of our method is illustrated through some numerical experiments. We also compare our results with those obtained by a standard finite difference method as well as other works seen in the literature. In addition, we provide a novel proof for the bounds on partial derivatives of the solution of the continuous problem.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Applied Mathematics and Computation - Volume 217, Issue 9, 1 January 2011, Pages 4728–4739
نویسندگان
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