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＜電子ブック＞
Multidimensional Weakly Singular Integral Equations / by Gennadi Vainikko
(Lecture Notes in Mathematics. ISSN:16179692 ; 1549)

版	1st ed. 1993.
出版者	(Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer)
出版年	1993
大きさ	XII, 168 p : online resource
著者標目	*Vainikko, Gennadi author SpringerLink (Online service)
件　名	LCSH:Mathematical analysis LCSH:Numerical analysis FREE:Analysis FREE:Numerical Analysis
一般注記	Some problems leading to multidimensional weakly singular integral equations -- Preliminaries -- Smoothness of the solution -- Outlines of the discrete convergence theory -- Piecewise constant collocation and related methods -- Composite cubature algorithms -- Higher order methods -- Nonlinear integral equation The final aim of the book is to construct effective discretization methods to solve multidimensional weakly singular integral equations of the second kind on a region of Rn e.g. equations arising in the radiation transfer theory. To this end, the smoothness of the solution is examined proposing sharp estimates of the growth of the derivatives of the solution near the boundary G. The superconvergence effect of collocation methods at the collocation points is established. This is a book for graduate students and researchers in the fields of analysis, integral equations, mathematical physics and numerical methods. No special knowledge beyond standard undergraduate courses is assumed HTTP:URL=https://doi.org/10.1007/BFb0088979

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