K. Eshkuvatov, Zainidin and Nik Long, Nik Mohd Asri (2010) Approximating the singular integrals of Cauchy type with weight function on the interval. Journal of Computational and Applied Mathematics . ISSN 0377-0427
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Official URL: http://dx.doi.org/10.1016/j.cam.2010.09.013
It is known that the solutions of characteristic singular integral equations (SIEs) are expressed in terms of singular integrals of Cauchy type with weight functions w (x) = (1 + x)ν (1 - x)μ, where ν = ± frac(1, 2), μ = ± frac(1, 2). New quadrature formulas (QFs) are presented to approximate the singular integrals (SIs) of Cauchy type for all solutions of characteristic SIE on the interval [- 1, 1]. Linear spline interpolation, modified discrete vortex method and product quadrature rule are utilized to construct the QFs. Estimation of errors are obtained in the classes of functions Hα ([- 1, 1], A) and C1 ([- 1, 1]). It is found that the numerical results are very stable even for the cases of semi-bounded and unbounded solutions of singular integral equation of the first kind.
|Keyword:||Approximation, Discrete vortex method, Quadrature formula, Singular integral, Singular integral equations, Spline|
|Faculty or Institute:||Institute for Mathematical Research|
|Deposited By:||Erni Suraya Abdul Aziz|
|Deposited On:||17 Dec 2010 08:49|
|Last Modified:||17 Dec 2010 08:53|
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