Peter Junghanns; Steffen Roch; Bernd Silbermann : Collocation methods for systems of Cauchy singular integral equations on an interval

Author(s) :

Peter Junghanns; Steffen Roch; Bernd Silbermann

Title :

Collocation methods for systems of Cauchy singular integral equations on an interval

Electronic source :

[gzipped ps-file] 172 kB

Preprint series

Technische Universität Chemnitz, Fakultät für Mathematik (Germany). Preprint 2000-8, 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 :

Necessary and sufficient conditions for the stability of collocation methods with respect to Chebyshev nodes of first and second kind for Cauchy singular integral equations with piecewise continuous coefficients, given on an interval, in the scalar and in the system case are established. Moreover, the behaviour of the singular values of the matrices of the discrete equations is considered.

Keywords :

Cauchy singular integral equation, collocation method, stability, Banch algebra techniques, singular value distribution

Language :

english

Publication time :

9/2000