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On the uniform convergence of a collocation method for a class of singular integral equations. (English) Zbl 0629.65139
The author establishes uniform convergence of collocation methods for singular integral equations of the form \[ a\phi (x)+(b/\pi)\int^{1}_{-1}(\phi (t)/(t-x))dt+\int^{1}_{- 1}k(x,t)\phi (t)dt=f(x),\quad -1<x<1 \] for which k(x,t) and f(x) are Hölder continuous. The Jacobi polynomials \(\{P_ n^{(\alpha,\beta)}\}\) are used as basis elements and the zeros of Chebyshev polynomials of the first kind as collocation points. Rates of convergence are also established and numerical examples presented to illustrate the results obtained.
Reviewer: D.A.Quinney

MSC:
65R20 Numerical methods for integral equations
45E05 Integral equations with kernels of Cauchy type
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