Approximating the singular integrals of Cauchy type with weight function on the interval

作者：Eshkuvatov Z K^*; Long N M A Nik

来源：Journal of Computational and Applied Mathematics, 2011, 235(16): 4742-4753.

DOI：10.1016/j.cam.2010.09.013

• Singular integral
• Singular integral equations
• Quadrature formula
• Discrete vortex method
• Approximation
• Spline

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)(nu)(1-x)(mu), where nu = +/- 1/2, mu = +/- 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 left prerpendicular-1, 1right perpendicular. 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 H-alpha(inverted right perpendicular-1, 1inverted left perpendicular, A) and C-1 (left prerpendicular-1. 1right prerpendicular). 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.

• 出版日期2011-6-15