Optimal quadrature formulas for approximate solution of the first kind singular integral equation with Cauchy kernel
DOI:
https://doi.org/10.24193/subbmath.2022.3.15Keywords:
Optimal quadrature formulas, the extremal function, Sobolev space, optimal coefficients, Cauchy type singular integral, weight function, singular integral equation.Abstract
In the present paper in L(m)(−1, 1) space the optimal quadrature formulas with derivatives are constructed for approximate solution of a singular integral equation of the first kind with Cauchy kernel. Approximate solution of the singular integral equation is obtained applying the optimal quadrature formulas. Explicit forms of coefficients for the of optimal quadrature formulas are obtained. Some numerical results are presented.
Mathematics Subject Classification (2010): 65D30, 65D32, 65R20.
Received 16 August 2021; Accepted 27 April 2022.
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