Numerical solution of various cases of Cauchy type singular integral equation

2014 ◽  
Vol 230 ◽  
pp. 200-207 ◽  
Author(s):  
Amit Setia
Keyword(s):  
Integral Equation ◽  
Singular Integral Equation ◽  
Numerical Solution ◽  
Singular Integral ◽  
Cauchy Type

scholarly journals Numerical Solution of the Cauchy-Type Singular Integral Equation with a Highly Oscillatory Kernel Function

Mathematics ◽  
2019 ◽  
Vol 7 (10) ◽  
pp. 872 ◽  
Author(s):  
◽  
Shuhuang Xiang ◽  
Guidong Liu
Keyword(s):  
Integral Equation ◽  
Singular Integral Equation ◽  
Numerical Solution ◽  
Integral Equations ◽  
Kernel Function ◽  
Singular Integral ◽  
Singular Integral Equations ◽  
Cauchy Type ◽  
Error Analyses ◽  
Highly Oscillatory

This paper aims to present a Clenshaw–Curtis–Filon quadrature to approximate thesolution of various cases of Cauchy-type singular integral equations (CSIEs) of the second kind witha highly oscillatory kernel function. We adduce that the zero case oscillation (k = 0) proposed methodgives more accurate results than the scheme introduced in Dezhbord at el. (2016) and Eshkuvatovat el. (2009) for small values of N. Finally, this paper illustrates some error analyses and numericalresults for CSIEs.

scholarly journals Решение электродинамической задачи для микрополосковой излучающей структуры с киральной подложкой

2018 ◽  
Vol 44 (11) ◽  
pp. 80
Author(s):  
М.А. Бузова ◽  
Д.С. Клюев ◽  
М.А. Минкин ◽  
А.М. Нещерет ◽  
Ю.В. Соколова
Keyword(s):  
Integral Equation ◽  
Singular Integral Equation ◽  
Singular Integral ◽  
Surface Current ◽  
Longitudinal Component ◽  
Cauchy Type ◽  
Surface Current Density ◽  
Electrodynamic Problem ◽  
Type Singularity ◽  
Different Types

AbstractWe present a solution of the electrodynamic problem for a microstrip radiating structure with a substrate of a chiral metamaterial using the singular integral representation of the field, which in turn is reduced to a singular integral equation with the Cauchy-type singularity relative to the longitudinal component of the surface current density. Graphs of the current distribution for different types of substrates and the chirality parameters of a substrate are given.

scholarly journals Numerical solution of a weakly singular integral equation by the method of orthogonal polynomials

2021 ◽  
pp. 98-103
Author(s):  
Sergei M. Sheshko
Keyword(s):  
Integral Equation ◽  
Approximate Solution ◽  
Singular Integral Equation ◽  
Orthogonal Polynomials ◽  
Numerical Solution ◽  
Singular Integral ◽  
Algebraic Equations ◽  
Linear Algebraic Equations ◽  
Expansion Coefficients ◽  
Analytical Expressions

A scheme is constructed for the numerical solution of a singular integral equation with a logarithmic kernel by the method of orthogonal polynomials. The proposed schemes for an approximate solution of the problem are based on the representation of the solution function in the form of a linear combination of the Chebyshev orthogonal polynomials and spectral relations that allows to obtain simple analytical expressions for the singular component of the equation. The expansion coefficients of the solution in terms of the Chebyshev polynomial basis are calculated by solving a system of linear algebraic equations. The results of numerical experiments show that on a grid of 20 –30 points, the error of the approximate solution reaches the minimum limit due to the error in representing real floating-point numbers.

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