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.

Continuum eigenfunctions for a hard-sphere gas

1968 ◽  
Vol 46 (20) ◽  
pp. 2287-2290 ◽  
Author(s):  
M. Rahman ◽  
M. K. Sundaresan
Keyword(s):  
Integral Equation ◽  
Boltzmann Equation ◽  
Singular Integral Equation ◽  
Integral Equations ◽  
Singular Integral ◽  
Hard Sphere ◽  
Singular Integral Equations ◽  
Cauchy Type ◽  
Fredholm Equations ◽  
Linearized Boltzmann Equation

The singular integral equation resulting from the linearized Boltzmann equation for a hard-sphere gas in the continuous region is reduced to two Fredholm equations of first and second kinds using the theory of singular integral equations with Cauchy-type singularities.

scholarly journals A convergence theorem for singular integral equations

1981 ◽  
Vol 22 (4) ◽  
pp. 539-552 ◽  
Author(s):  
David Elliott
Keyword(s):  
Integral Equation ◽  
Singular Integral Equation ◽  
Integral Equations ◽  
Singular Integral ◽  
Sufficient Conditions ◽  
Singular Integral Equations ◽  
Convergence Theory ◽  
Cauchy Kernel ◽  
Algebraic Equations ◽  
Linear Algebraic Equations

AbstractThe principal result of this paper states sufficient conditions for the convergence of the solutions of certain linear algebraic equations to the solution of a (linear) singular integral equation with Cauchy kernel. The motivation for this study has been the need to provide a convergence theory for a collocation method applied to the singular integral equation taken over the arc (−1, 1). However, much of the analysis will be applicable both to other approximation methods and to singular integral equations taken over other arcs or contours. An estimate for the rate of convergence is also given.

Regularization Method for Complete Singular Integral Equation with Hilbert Kernel on Open Arcs

2013 ◽  
Vol 765-767 ◽  
pp. 643-646
Author(s):  
Li Xia Cao
Keyword(s):  
Integral Equation ◽  
Singular Integral Equation ◽  
Integral Equations ◽  
Singular Integral ◽  
Regularization Method ◽  
Singular Integral Equations ◽  
Noether Theorem ◽  
Hilbert Kernel

We considered the regularization method for a kind of complete singular integral equation with Hilbert kernel on open arcs lying in a period strip. And based on this, we obtained the solvable Noether theorem for this kind of complete singular integral equations.

On an approximate solution of a class of surface singular integral equations of the first kind

2020 ◽  
Vol 27 (1) ◽  
pp. 97-102 ◽  
Author(s):  
Elnur H. Khalilov
Keyword(s):  
Integral Equation ◽  
Approximate Solution ◽  
Singular Integral Equation ◽  
Helmholtz Equation ◽  
Boundary Value Problems ◽  
Integral Equations ◽  
Singular Integral ◽  
Singular Integral Equations ◽  
Neumann Boundary ◽  
Neumann Boundary Value Problems

AbstractIn this work, a method for calculating an approximate solution of a singular integral equation of first kind is presented for the Neumann boundary value problems for the Helmholtz equation.

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