کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4641651 1341316 2009 11 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Modified product cubature formulae
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات کاربردی
پیش نمایش صفحه اول مقاله
Modified product cubature formulae
چکیده انگلیسی

In the univariate case, there is a well-developed theory on the error estimation of the quadrature formulae for integrands from the Sobolev classes of functions. It is based on the Peano kernel representation of linear functionals, which yields sharp error bounds for the quadrature remainder. The product cubature formulae are the usual tool for the approximation of a double integral over a rectangular domain. In this paper we suggest a modification of the product cubature formulae, based on blending interpolation of bivariate functions. Besides the usual point evaluations, the modified cubature formulae involve few line integrals. Our approach allows application of the Peano kernel theory for derivation of error bounds for both standard cubature formulae and their modifications. Sufficient conditions for the definiteness of the modified product cubature formulae are given, and some classes of integrands are specified, for which a product cubature formula is inferior to its modified version.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Computational and Applied Mathematics - Volume 224, Issue 2, 15 February 2009, Pages 465–475
نویسندگان
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