Galerkin trigonometric wavelet methods for the natural boundary integral equations

摘要

A simply supported boundary value problem of biharmonic equations in the unit 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 [Math. Comput. 65 (1996) 683–722] as trial functions are used to its Galerkin discretization with 2J+1 degrees of freedom on the boundary. It is proved that the stiffness matrix is a block diagonal matrix and its diagonal elements are some symmetric and block circulant submatrices. The simple computational formulae of the entries in stiffness matrix are obtained. These show that we only need to compute 2(2J+J+1) elements of a 2J+2×2J+2 stiffness matrix. The error estimates for the approximation solutions are established. Finally, numerical examples are given.