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