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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) ]
- 45F15 [ Systems of singular linear integral equations ]
- 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
