Author	Vainikko, Gennadi. author
Title	Multidimensional Weakly Singular Integral Equations [electronic resource] / by Gennadi Vainikko
Imprint	Berlin, Heidelberg : Springer Berlin Heidelberg, 1993
Connect to	http://dx.doi.org/10.1007/BFb0088979
Descript	XII, 168 p. online resource

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

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

1. Mathematics
2. Mathematical analysis
3. Analysis (Mathematics)
4. Numerical analysis
5. Mathematics
6. Analysis
7. Numerical Analysis