Approximate Solution of a Singular Integral Equation Using the Sobolev Method
Kh. M. ShadimetovTashkent State Transport University, 100167, Tashkent, UzbekistanD.M. AkhmedovNational University of Uzbekistan, 100174, Tashkent, Uzbekistan
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Annotatsiya
In the present paper in the $$L_{2}^{(m)}(-1,1)$$ 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 for the singular integral equation is obtained, applying the optimal quadrature formulas (OQF). Explicit forms of coefficients for the optimal quadrature formulas are obtained. Some numerical results are presented.
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