An effective method for approximating the solution of singular integral equations with Cauchy kernel type
Authors
Abstract:
In present paper, a numerical approach for solving Cauchy type singular integral equations is discussed. Lagrange interpolation with Gauss Legendre quadrature nodes and Taylor series expansion are utilized to reduce the computation of integral equations into some algebraic equations. Finally, five examples with exact solution are given to show efficiency and applicability of the method. Also, we give the maximum of computed absolute errors for some examples.
similar resources
An effective collocation technique to solve the singular Fredholm integral equations with Cauchy kernel
*Correspondence: [email protected] Department of Mathematics, Islamic Azad University, Hamedan Branch, Hamedan, Iran Abstract In this paper, an effective numerical method to solve the Cauchy type singular Fredholm integral equations (CSFIEs) of the first kind is proposed. The collocation technique based on Bernstein polynomials is used for approximation the solution of various cases of CSFIE...
full textCAS WAVELET METHOD FOR THE NUMERICAL SOLUTION OF BOUNDARY INTEGRAL EQUATIONS WITH LOGARITHMIC SINGULAR KERNELS
In this paper, we present a computational method for solving boundary integral equations with loga-rithmic singular kernels which occur as reformulations of a boundary value problem for the Laplacian equation. Themethod is based on the use of the Galerkin method with CAS wavelets constructed on the unit interval as basis.This approach utilizes the non-uniform Gauss-Legendre quadrature rule for ...
full textApproximate solution of singular integral equations of the first kind with Cauchy kernel
In this work a study of efficient approximate methods for solving the Cauchy type singular integral equations (CSIEs) of the first kind, over a finite interval, is presented. In the solution, Chebyshev polynomials of the first kind, Tn(x)Tn(x), second kind, Un(x)Un(x), third kind, Vn(x)Vn(x), and fourth kind, Wn(x)Wn(x), corresponding to respective weight functions View the MathML sourceW(1)(x)...
full textNumerical Solution of Singular Integro-differential Equations with Cauchy Kernel
The main purpose of this article is to present an approximation method of for singular integrodifferential equations with Cauchy kernel in the most general form under the mixed conditions in terms of the second kind Chebyshev polynomials. This method transforms mixed singular integro-differential equations with Cauchy kernel and the given conditions into matrix equation and using the zeroes of ...
full textOn the solution of integral equations of the first kind with singular kernels of Cauchy-type
Abstract Two efficient quadrature formulae have been developed for evaluating numerically certain singular integral equations of the first kind over the finite interval [-1,1]. Central to this work is the application of four special cases of the Jacobi polynomials P n (x), whose zeros served as interpolation and collocation nodes: (i) α = β = −2 , Tn(x), the first kind Chebyshev polynomials (ii...
full textA Nodal Spline Collocation Method for the Solution of Cauchy Singular Integral Equations
In this paper we introduce a nodal spline collocation method for the numerical solution of Cauchy singular integral equations. Uniform error bounds of the approximate solution are provided and some numerical examples are presented. c © 2008 European Society of Computational Methods in Sciences and Engineering
full textMy Resources
Journal title
volume 7 issue 1
pages 102- 112
publication date 2018-04-01
By following a journal you will be notified via email when a new issue of this journal is published.
Hosted on Doprax cloud platform doprax.com
copyright © 2015-2023