Multidimensional Weakly Singular Integral Equations

1993
ISBN: 978-3-540-56878-0
Verlag: Springer Berlin Heidelberg

Buch, Englisch, Band 1549, 168 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 283 g

Reihe: Lecture Notes in Mathematics

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.

Zielgruppe

Research

Autoren/Hrsg.

Vainikko, Gennadi

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Integralrechnungen- und -gleichungen

Inhaltsverzeichnis

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.