CAS Wavelet Method for the Numerical Solution of Boundary Integral Equations with Logarithmic Singular Kernels
- M. Shamooshaky
1 - Pouria Assar2
- Hojatollah Adibi*3
- Department of Mathematics, Imam Hossein University, P.O. Box 16895-198, Tehran, Iran
- Department of Applied Mathematics, Faculty of Mathematics and Computer Science, Amirkabir University of Technology, No. 424, Hafez Ave., Tehran 15914, Iran
- Department of Mathematics, Central Tehran Branch, Islamic Azad University, Iran
Received: 09-02-2014
Revised: 21-04-2014
Accepted: 11-06-2014
Published in Issue 21-03-2014
Copyright (c) 2024 International Journal of Mathematical Modeling & Computations
This work is licensed under a Creative Commons Attribution 4.0 International License.
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Abstract
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 non-uniform 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.