SincNyström method for numerical solution of onedimensional Cauchy singular integral equation given on a smooth arc in the complex plane
Authors:
Bernard Bialecki and Frank Stenger
Journal:
Math. Comp. 51 (1988), 133165
MSC:
Primary 65R20
MathSciNet review:
942147
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Abstract: We develop a numerical method based on Sinc functions to obtain an approximate solution of a onedimensional Cauchy singular integral equation (CSIE) over an arbitrary, smooth, open arc L of finite length in the complex plane. At the outset, we reduce the CSIE to a Fredholm integral equation of the second kind via a regularization procedure. We then obtain an approximate solution to the Fredholm integral equation by means of Nyström's method based on a Sinc quadrature rule. We approximate the matrix and righthand side of the resulting linear system by an efficient method of computing the Cauchy principal value integrals. The error of an Npoint approximation converges to zero at the rate , as , provided that the coefficients of the CSIE are analytic in a region D containing the arc L and satisfy a Lipschitz condition in D.
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DOI:
http://dx.doi.org/10.1090/S0025571819880942147X
PII:
S 00255718(1988)0942147X
Keywords:
Cauchy singular integral equation
Article copyright:
© Copyright 1988
American Mathematical Society
