Numerical solution of various cases of Cauchy type singular integral equation

Setia, Amit

doi:10.1016/j.amc.2013.12.114

Cited by 16 publications

(8 citation statements)

References 14 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…A reliable, yet very simple, numerical method to solve different cases of a singular Cauchy-type integral equation is developed in [5]. For this purpose, first Bernstein polynomials are derived, which are used to approximate a solution of the given singular integral equation.…”

Section: Construction Of Interpolation Methods For Numerical Solution mentioning

confidence: 99%

Construction of interpolation method for numerical solution of the Cauchy's problem

Bihun

Tsehelyk

2017

EEJET

View full text Add to dashboard Cite

Section: Construction Of Interpolation Methods For Numerical Solution mentioning

confidence: 99%

Construction of interpolation method for numerical solution of the Cauchy's problem

Bihun

Tsehelyk

2017

EEJET

View full text Add to dashboard Cite

“…Bonis and Laurita [14] have proposed a Nyström method to approximate the solutions of Cauchy singular integral equations with constant coefficients having a negative index. Recently Setia [15] investigated a numerical method for approximate solution of Cauchy type singular integral equation of the first kind over [−1, 1] and it is based on Bernstein polynomial and so on [16].…”

Section: Introductionmentioning

confidence: 99%

A new efficient method for cases of the singular integral equation of the first kind

Lotfi

Mahdiani

2016

Journal of Computational and Applied Mathematics

View full text Add to dashboard Cite

Various cases of Cauchy type singular integral equation of the first kind occur rather frequently in mathematical physics and possess very unusual properties. These equations are usually difficult to solve analytically, and it is required to obtain approximate solutions. This paper investigates the numerical solution of various cases of Cauchy type singular integral equations using reproducing kernel Hilbert space (RKHS) method. The solution u(x) is represented in the form of a series in the reproducing kernel space, afterwards the n-term approximate solution u n (x) is obtained and it is proved to converge to the exact solution u(x). The major advantage of the method is that it can produce good globally smooth approximate solutions. Moreover, in this paper, an efficient error estimation of the RKHS method is introduced. Finally, numerical experiments show that our reproducing kernel method is efficient.

show abstract

“…Another technique is based on analytic continuation of the integral if the integrand f (x) is analytic in the complex region [14]. As far as for k = 0 solution methods and properties of the solution for relative non-homogenous integrals have been discussed by using Brestain polynomials and Chebyshev polynoimals of all four kinds in [3,15].…”

Section: Introductionmentioning

confidence: 99%

Approximation to Logarithmic-Cauchy Type Singular Integrals with Highly Oscillatory Kernels

Saira

Xiang

2019

Symmetry

View full text Add to dashboard Cite

In this paper, a fast and accurate numerical Clenshaw-Curtis quadrature is proposed for the approximation of highly oscillatory integrals with Cauchy and logarithmic singularities, ⨍ − 1 1 f ( x ) log ( x − α ) e i k x x − t d x , t ∉ ( − 1 , 1 ) , α ∈ [ − 1 , 1 ] for a smooth function f ( x ) . This method consists of evaluation of the modified moments by stable recurrence relation and Cauchy kernel is solved by steepest descent method that transforms the oscillatory integral into the sum of line integrals. Later theoretical analysis and high accuracy of the method is illustrated by some examples.

show abstract

Numerical solution of various cases of Cauchy type singular integral equation

Cited by 16 publications

References 14 publications

Construction of interpolation method for numerical solution of the Cauchy's problem

Construction of interpolation method for numerical solution of the Cauchy's problem

A new efficient method for cases of the singular integral equation of the first kind

Approximation to Logarithmic-Cauchy Type Singular Integrals with Highly Oscillatory Kernels

Contact Info

Product

Resources

About