Uniform Convergence of a Collocation Method for the Numerical Solution of Cauchy-Type Singular Integral Equations: A Generalization

1992 ◽  
Vol 12 (1) ◽  
pp. 31-45 ◽  
Author(s):  
J. A. CUMINATO
Keyword(s):  
Uniform Convergence ◽  
Numerical Solution ◽  
Integral Equations ◽  
Collocation Method ◽  
Singular Integral ◽  
Singular Integral Equations ◽  
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.

Approximate Solution of a Singular Integral Cauchy-Kernel Equation of the First Kind

2010 ◽  
Vol 10 (4) ◽  
pp. 359-367 ◽  
Author(s):  
M. Kashfi ◽  
S. Shahmorad
Keyword(s):  
Approximate Solution ◽  
Numerical Solution ◽  
Integral Equations ◽  
Singular Integral ◽  
Chebyshev Polynomials ◽  
Estimation Error ◽  
Singular Integral Equations ◽  
Cauchy Kernel ◽  
Cauchy Type ◽  
Finite Segment

AbstractIn this paper we present a method for the numerical solution of Cauchy type singular integral equations of the first kind on a finite segment which is unbounded at the end points of the segment. Chebyshev polynomials of the first and second kinds are used to derive an approximate solution. Moreover, an estimation error is computed for the approximate solution.

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