Multidimensional Weakly Singular Integral Equations

Gennadi Vainikko (auth.)3540568786, 9783540568780, 0387568786

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.

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Table of contents :
Some problems leading to multidimensional weakly singular integral equations….Pages 1-9
Preliminaries….Pages 10-23
Smoothness of the solution….Pages 24-50
Outlines of the discrete convergence theory….Pages 51-59
Piecewise constant collocation and related methods….Pages 60-93
Composite cubature algorithms….Pages 94-111
Higher order methods….Pages 112-136
Nonlinear integral equation….Pages 137-144