Multidimensional Weakly Singular Integral Equations
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 gradu…
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- Full title :Multidimensional Weakly Singular Integral Equations / by Gennadi Vainikko.
Summary
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.
Read More ↓Edition Statements
- Publication Date:1993.
Publication Statements
- Publisher(s):Imprint, Springer, Springer Berlin Heidelberg
- Place of Publication:Berlin, Heidelberg
- Language:eng
- Publication Date:1993.
The Physical Object
- Description:1 online resource (xii, 168 pages)
Edition Identifiers
- ISBN:9783540568780, 9783540477730, 354047773X, 3540568786
- DOI:10.1007/BFb0088979
- oclc:on1058134790
- LC Classification:QA299.6-433
- Dewey Decimal:515
Table of Contents
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.
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