CAS WAVELET METHOD FOR THE NUMERICAL SOLUTION OF BOUNDARY INTEGRAL EQUATIONS WITH LOGARITHMIC SINGULAR KERNELS

Subject Areas : International Journal of Mathematical Modelling & Computations

Hojatollah Adibi ¹ , M. Shamooshaky ² , Pouria Assar ³

1 - Department of Mathematics, amirkabir University,Iran Department of mathematics, IAU,TCB Iran, Islamic Republic of
2 -
3 - Amirkabir University of Technology

Received: 2016-04-15 Accepted : 2016-04-15 Published : 2014-03-21

Keywords: Galerkin Method, CAS wavelet, Boundary integral equation, Logarithmic singular kernel, Laplacian equation, sparse matrix,

Abstract :

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 approximating logarithm-like singularintegrals and so reduces the solution of boundary integral equations to the solution of linear systems of algebraicequations. The properties of CAS wavelets are used to make the wavelet coe±cient matrices sparse, which eventuallyleads to the sparsity of the coe±cient matrix of the obtained system. Finally, the validity and e±ciency of the newtechnique are demonstrated through a numerical example.