CAS Wavelet Method for the Numerical Solution of Boundary Integral Equations with Logarithmic Singular Kernels
نویسندگان
چکیده
In this paper, we present a computational method for solving boundary integral equations with logarithmic singular kernels which occur as reformulations of a boundary value problem for Laplace’s equation. The method is based on the use of the Galerkin method with CAS wavelets constructed on the unit interval as basis. This approach utilizes the nonuniform Gauss-Legendre quadrature rule for approximating logarithm-like singular integrals and so reduces the solution of boundary integral equations to the solution of linear systems of algebraic equations. The properties of CAS wavelets are used to make the wavelet coefficient matrices sparse, which eventually leads to the sparsity of the coefficient matrix of the obtained system. Finally, the validity and efficiency of the new technique are demonstrated through a numerical example. Received: 9 February 2014, Revised: 21 April 2014, Accepted: 11 June 2014.
منابع مشابه
CAS 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 ...
متن کاملNUMERICAL APPROACH TO SOLVE SINGULAR INTEGRAL EQUATIONS USING BPFS AND TAYLOR SERIES EXPANSION
In this paper, we give a numerical approach for approximating the solution of second kind Volterra integral equation with Logarithmic kernel using Block Pulse Functions (BPFs) and Taylor series expansion. Also, error analysis shows efficiency and applicability of the presented method. Finally, some numerical examples with exact solution are given.
متن کاملApplying fuzzy wavelet like operator to the numerical solution of linear fuzzy Fredholm integral equations and error analysis
In this paper, we propose a successive approximation method based on fuzzy wavelet like operator to approximate the solution of linear fuzzy Fredholm integral equations of the second kind with arbitrary kernels. We give the convergence conditions and an error estimate. Also, we investigate the numerical stability of the computed values with respect to small perturbations in the first iteration....
متن کاملA finite difference method for the smooth solution of linear Volterra integral equations
The present paper proposes a fast numerical method for the linear Volterra integral equations withregular and weakly singular kernels having smooth solutions. This method is based on the approx-imation of the kernel, to simplify the integral operator and then discretization of the simpliedoperator using a forward dierence formula. To analyze and verify the accuracy of the method, weexamine samp...
متن کاملSolving Volterra Integral Equations of the Second Kind with Convolution Kernel
In this paper, we present an approximate method to solve the solution of the second kind Volterra integral equations. This method is based on a previous scheme, applied by Maleknejad et al., [K. Maleknejad and Aghazadeh, Numerical solution of Volterra integral equations of the second kind with convolution kernel by using Taylor-series expansion method, Appl. Math. Comput. (2005)] to gain...
متن کامل