Galerkin trigonometric wavelet methods for the natural boundary integral equations

A simply supported boundary value problem of biharmonic equations in the un it disk is reduced into an equivalent second kind natural boundary integral equation (NBIE) with hypersingular kernel (in the sense of Hadamard finite part). Trigonometric Hermite interpolatory wavelets introduced by Quak [Ma th. Comput. 65 (1996) 683-722] as trial functions are used to its Galerkin discretization with 2(J+1) degrees of freedom on the boundary. It is proved that the stiffness matrix is a block diagonal matrix and its diagonal elem ents are some symmetric and block circulant submatrices. The simple computa tional formulae of the entries in stiffness matrix are obtained. These show that we only need to compute 2(2(J) +J + 1) elements of a 2(J+2) x 2(J+2) stiffness matrix. The error estimates for the approximation solutions are e stablished. Finally, numerical examples are given. (C) 2001 Elsevier Scienc e Inc. All rights reserved.