کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4631769 1340629 2010 11 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
A new finite difference representation for Poisson’s equation on R3R3 from a contour integral
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات کاربردی
پیش نمایش صفحه اول مقاله
A new finite difference representation for Poisson’s equation on R3R3 from a contour integral
چکیده انگلیسی

In this paper, we propose a new finite difference representation for solving a Dirichlet problem of Poisson’s equation on R3R3. The key idea of the new approach is to represent the solution with a contour integral connecting the nodal values of each local domain centered at each isolated grid node, which is based on the boundary integral equation on the local domain, and calculate the contour integral using a piecewise linear interpolation of the solution. A superconvergence of the scheme is analyzed using a maximum principle and a priori estimate for the finite difference operator. The convergence behavior is comparable to that of standard finite difference methods on rectangle grids, and a superconvergence property is attained when the solution u   is in the function class C2,α(Ω¯)∪C3(Ω¯), 0 < α < 1. Also, if u∈C3,1(Ω¯), the standard O(h2) convergence is obtained.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Applied Mathematics and Computation - Volume 217, Issue 8, 15 December 2010, Pages 3624–3634
نویسندگان
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