Optimal quadrature formulas for approximate solution of the first kind singular integral equation of 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 equationAbstract
In the present paper in $L_2^{(m)}(-1,1)$ 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 is obtained applying optimal quadrature formulas (OQF). Explicit forms for the of OQF`s are obtained. Some numerical results are presented.
