Method of mechanical quadratures for solving singular integral equations of various types

The method of mechanical quadratures is proposed as a common approach intended for solving the integral equations defined on finite intervals and containing Cauchy-type singular integrals. This method can be used to solve singular integral equations of the first and second kind, equations with gener...

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Bibliographic Details
Published in:Journal of physics. Conference series 2018-04, Vol.991 (1), p.12070
Main Authors: Sahakyan, A V, Amirjanyan, H A
Format: Article
Language:English
Subjects:
Differential equations
Integral equations
Integrals
Linear algebra
Mathematical analysis
Physics
Quadratures
Singular integral equations
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Summary:The method of mechanical quadratures is proposed as a common approach intended for solving the integral equations defined on finite intervals and containing Cauchy-type singular integrals. This method can be used to solve singular integral equations of the first and second kind, equations with generalized kernel, weakly singular equations, and integro-differential equations. The quadrature rules for several different integrals represented through the same coefficients are presented. This allows one to reduce the integral equations containing integrals of different types to a system of linear algebraic equations.
ISSN:1742-6588
1742-6596
DOI:10.1088/1742-6596/991/1/012070