TY  - BOOK
AU  - Vainikko,Gennadi
ED  - SpringerLink (Online service)
TI  - Multidimensional Weakly Singular Integral Equations
T2  - Lecture Notes in Mathematics,
SN  - 9783540477730
AV  - QA299.6-433 
U1  - 515 23
PY  - 1993///
CY  - Berlin, Heidelberg
PB  - Springer Berlin Heidelberg
KW  - Mathematics
KW  - Global analysis (Mathematics)
KW  - Numerical analysis
KW  - Analysis
KW  - Numerical Analysis
N1  - 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
N2  - 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
UR  - http://dx.doi.org/10.1007/BFb0088979
ER  -