scholarly journals Singularity subtraction in the numerical solution of integral equations

1981 ◽  
Vol 22 (4) ◽  
pp. 408-418 ◽  
Author(s):  
P. M. Anselone
Keyword(s):  
Numerical Solution ◽  
Numerical Integration ◽  
Integral Equations ◽  
Error Bounds ◽  
Subtraction Technique ◽  
Weakly Singular Kernel ◽  
Numerical Examples ◽  
Weakly Singular ◽  
Convergence Results ◽  
Numerical Integration Procedure

AbstractThe singularity subtraction technique described by Kantorovich and Krylov in [11] is designed to reduce or overcome the effect of a weakly singular kernel in the numerical solution of integral equations. First, the equation is rearranged in such a way that the singularity of the kernel is at least partially cancelled by the smoothness of the solution, and then numerical integration is applied. We present convergence results and error bounds under general conditions on the nature of the singularity and the numerical integration procedure. Numerical examples demonstrate the benefit of the singularity subtraction technique.

scholarly journals An efficient method for the numerical solution of the nonlinear Hammerstein fractional integral equations

Filomat ◽  
2021 ◽  
Vol 35 (2) ◽  
pp. 419-429
Author(s):  
Ahmadabadi Nili ◽  
M.R. Velayati
Keyword(s):  
Error Analysis ◽  
Numerical Solution ◽  
Integral Equations ◽  
Efficient Method ◽  
Fractional Integral ◽  
Singular Integrals ◽  
Computational Cost ◽  
Picard Iteration ◽  
Numerical Examples ◽  
Weakly Singular

In this paper, we present a numerical method for solving nonlinear Hammerstein fractional integral equations. The method approximates the solution by Picard iteration together with a numerical integration designed for weakly singular integrals. Error analysis of the proposed method is also investigated. Numerical examples approve its efficiency in terms of accuracy and computational cost.

scholarly journals On integral equations with Weakly Singular kernel by using Taylor series and Legendre polynomials

Open Physics ◽  
2015 ◽  
Vol 13 (1) ◽  
Author(s):  
Esmail Babolian ◽  
Danial Hamedzadeh ◽  
Hossein Jafari ◽  
Asghar Arzhang Hajikandi ◽  
Dumitru Baleanu
Keyword(s):  
Numerical Solution ◽  
Integral Equations ◽  
Taylor Series ◽  
Unknown Function ◽  
Legendre Polynomials ◽  
Second Order ◽  
Singular Kernel ◽  
Fredholm Integral Equations ◽  
Weakly Singular Kernel ◽  
Weakly Singular

AbstractThis paper is concerned with the numerical solution for a class of weakly singular Fredholm integral equations of the second kind. The Taylor series of the unknown function, is used to remove the singularity and the truncated Taylor series to second order of k(x, y) about the point (x

scholarly journals A linear approximation for solutions of Abel–Volterra integral equations

2020 ◽  
Vol 14 (2) ◽  
pp. 596-604
Author(s):  
Mostefa Nadir
Keyword(s):  
Integral Equations ◽  
Linear Approximation ◽  
Singular Integral ◽  
Volterra Integral Equations ◽  
New Technique ◽  
Numerical Examples ◽  
Weakly Singular

Abstract In this work, we present a modified linear approximation for solving the first and the second kind Abel–Volterra integral equations. This approximation was used by the author to approximate a weakly singular integral on the curve. Noting that this new technique gives a good approximation of these solutions compared with several methods in several numerical examples.

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