2016arXiv (Cornell University)Open access

Numerical methods for solution of singular integral equations

I. V. Boykov

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Abstract

This paper is devoted to overview of the authors works for numerical solution of singular integral equations (SIE), polysingular integral equations and multi-dimensional singular integral equations of the second kind. The authors investigated onsidered iterative - projective methods and parallel methods for solution of singular integral equations, polysingular integral equations and multi-dimensional singular integral equations. The paper is the second part of overview of the authors works devoted to numerical methods for calculation singular and hypersingular integrals \cite{Boy23} and to approximate methods for solution of singular integral equations.

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This paper is devoted to overview of the authors works for numerical solution of singular integral equations (SIE), polysingular integral equations and multi-dimensional singular integral equations of the second kind. The authors investigated onsidered iterative - projective methods and parallel methods for solution of singular integral equations, polysingular integral equations and multi-dimensional singular integral equations. The paper is the second part of overview of the authors works devoted to numerical methods for calculation singular and hypersingular integrals \cite{Boy23} and to approximate methods for solution of singular integral equations.

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Available abstract

This paper is devoted to overview of the authors works for numerical solution of singular integral equations (SIE), polysingular integral equations and multi-dimensional singular integral equations of the second kind. The authors investigated onsidered iterative - projective methods and parallel methods for solution of singular integral equations, polysingular integral equations and multi-dimensional singular integral equations. The paper is the second part of overview of the authors works devoted to numerical methods for calculation singular and hypersingular integrals \cite{Boy23} and to approximate methods for solution of singular integral equations.

Key concepts: Singular integral, Integral equation, Mathematics, Singular solution, Mathematical analysis, Volume integral, Volterra integral equation, Numerical analysis

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