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Quadrature formula for semi-bounded solution of characteristic singular integral equation of cauchy type
(Maltepe Üniversitesi, 2009) Eshkuvvatov, Z. K.; Long, N. M. A. Nik; Abdulkawi, M.
It is known that the solutions of characteristic singular integral equations (SIEs) are expressed in terms of singular integrals of Cauchy type with wight functions of the form w(x) = (x - a)º(b - x)¹ , where -1 < º; ¹ < 1: In this paper new quadrature formulas are presented to approximate singular integrals of Cauchy type for half bounded solution of characteristic SIEs on the interval [-1; 1]. Linear interpolation spline and modification discrete vortices method (MMDV) are used to construct quadrature formula. Estimations of error are obtained in the classes of functions H ([-1; 1]) and C1([-1; 1]). Numerical experiments are presented to show the validity of the method presented.