کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4976134 | 1365607 | 2007 | 9 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Gauss quadrature formula: An extension via interpolating orthogonal polynomials
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موضوعات مرتبط
مهندسی و علوم پایه
مهندسی کامپیوتر
پردازش سیگنال
پیش نمایش صفحه اول مقاله
چکیده انگلیسی
The n-point Gauss quadrature rule states thatâ«-11f(x)Ï(x)dx=âi=1nwif(zi)+Rn(f),where zi and wi, i=1,â¦,n, are called, respectively, the Gaussian nodes and weights. It is known that the formula is exact of degree 2n-1. We provide an extension of this rule by considering x=-1 and 1 as the pre-assigned nodes of certain order n1 and n2, respectively. For this, we construct interpolating orthogonal polynomials that make the suggested rule capable of utilizing the maximum information related to the value and derivatives of the integrand f at these points. Our proposed rule is different from Gauss-Lobatto and Gauss-Radau quadrature formulae, which also take care of these points to a certain extent. The results related to the degree of exactness and convergence are also presented. Some questions related to our proposed rule which may require further investigation are narrated as well.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of the Franklin Institute - Volume 344, Issue 5, August 2007, Pages 637-645
Journal: Journal of the Franklin Institute - Volume 344, Issue 5, August 2007, Pages 637-645
نویسندگان
M.A. Bokhari,