An Adaptive Trigonometric Wavelet-Galerkin Method for First Kind Boundary Integral Equations

This paper discussed the implementing and convergence of a efficient Galerkin method using trigonometric wavelets for solving first kind boundary integral equations with logarithmic kernels on unit circle boundary in 2 R . Trigonometric Hermit interpolatory wavelets introduced by Quak [7] as trial functions are used to its Galerkin discretization. It is shown that the stiffness matrix is sparse has very simple form, i.e. it is a block diagonal symmetrical matrix and The submatrices in diagonal blocks is circulant and solving a small linear system gives good results. Finally, the convergence results are illustrated with some numerical examples

Keywords:

Trigonometric Hermit wavelet , First kind boundary integral equations