Navigation

Inhalt Hotkeys
Fakultät für Mathematik
Fakultät für Mathematik
Peter Junghanns; Andreas Rathsfeld : A polynomial collocation method for Cauchy singular integral equations over the interval

Peter Junghanns; Andreas Rathsfeld : A polynomial collocation method for Cauchy singular integral equations over the interval


Author(s) :
Peter Junghanns; Andreas Rathsfeld
Title :
A polynomial collocation method for Cauchy singular integral equations over the interval
Electronic source :
[gzipped ps-file] 216 kB
Preprint series
Technische Universität Chemnitz, Fakultät für Mathematik (Germany). Preprint 2000-12, 2000
Mathematics Subject Classification :
45E05 [ Integral equations with kernels of Cauchy type ]
45F15 [ Systems of singular linear integral equations ]
45L05 [ Theoretical approximation of solutions of integral equations ]
45L10 [ Numerical approximation of solutions of integral equations ]
65R20 [ Integral equations (numerical methods) ]
Abstract :
A polynomial collocation method for the numerical solution of a singular intergal equation over the interval is considered. More precisely, the operator of the equation is supposed to be a weighted cauchy singular integral operator with piecewise continuous coefficients. Collocation with respect to the Chebyshev nodes of second kind is applied, while the trial space is a space of weighted algebraic polynomials. For the stability and convergence of this collocation in a weighted L^2 space, necessary and sufficient conditions are derived.
Keywords :
Cauchy singular integral equation, collocation method, stability, Banach algebra techniques
Language :
english
Publication time :
9/2000

Presseartikel