کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
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4631175 | 1340617 | 2011 | 12 صفحه PDF | دانلود رایگان |

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.
Journal: Applied Mathematics and Computation - Volume 217, Issue 9, 1 January 2011, Pages 4728–4739