Analysis of general quadrature methods for integral equations of the second kind期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

Analysis of general quadrature methods for integral equations of the second kind

Authors:	Ian H. Sloan

Affiliation:	(1) Institute for Physical Science and Technology, and Department of Physics and Astronomy, University of Maryland, 20742 College Park, Maryland, USA;(2) Present address: School of Mathematics, University of New South Wales, 2033 Sydney, N.S.W., Australia

Abstract:	Summary This paper is concerned with a class of approximation methods for integral equations of the form $y(t) = f(t) + intlimits_a^b {k(t,s)y(s)ds}$ , wherea andb are finite,f andy are continuous and the kernelk may be weakly singular. The methods are characterized by approximate equations of the form $y_n (t) = f(t) + sumlimits_{i = 1}^n {W_{ni} (t)y_n (s_{ni} )}$ ; such methods include the Nyström method and a variety of product-integration methods. A general convergence theory is developed for methods of this type. In suitable cases it has the feature that its application to a specific method depends only on a knowledge of convergence properties of the underlying quadrature rule. The theory is used to deduce convergence results, some of them new, for a number of specific methods.Work supported by the U.S. Department of Energy

Keywords:	AMS(MOS) 65R05 45B05 CR 5. 18
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