کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4629928 1340589 2012 11 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
The impact of smooth W-grids in the numerical solution of singular perturbation two-point boundary value problems
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات کاربردی
پیش نمایش صفحه اول مقاله
The impact of smooth W-grids in the numerical solution of singular perturbation two-point boundary value problems
چکیده انگلیسی

This paper develops a semi-analytic technique for generating smooth nonuniform grids for the numerical solution of singularly perturbed two-point boundary value problems. It is based on the usual idea of mapping a uniform grid to the desired nonuniform grid. We introduce the W-grid, which depends on the perturbation parameter ϵ ≪ 1. For problems on [0, 1] with a boundary layer at one end point, the local mesh width hi = xi+1 − xi, with 0 = x0 < x1 < ⋯ < xN = 1, is condensed at either 0 or 1. Two simple 2nd order finite element and finite difference methods are combined with the new mesh, and computational experiments demonstrate the advantages of the smooth W-grid compared to the well-known piecewise uniform Shishkin mesh. For small ϵ, neither the finite difference method nor the finite element method produces satisfactory results on the Shishkin mesh. By contrast, accuracy is vastly improved on the W-grid, which typically produces the nominal 2nd order behavior in L2, for large as well as small values of N, and over a wide range of values of ϵ. We conclude that the smoothness of the mesh is of crucial importance to accuracy, efficiency and robustness.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Applied Mathematics and Computation - Volume 218, Issue 10, 15 January 2012, Pages 6045–6055
نویسندگان
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