Article

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

Lobachevskii Journal of Mathematicsjournal2022en

ABI

Abstract

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.

Topics

Numerical methods in engineering Differential Equations and Boundary Problems Differential Equations and Numerical Methods

Identifiers

DOI: 10.1134/s1995080222050249

Citations and references

Cited by 27 16 references

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