HERMITE CUBIC SPLINE MULTI-WAVELET NATURAL BOUNDARY ELEMENT METHOD
Hermite三次样条多小波自然边界元法

The Neumann boundary value problem for the Laplacian equation on the upper half plane can be solved by natural boundary element method, but it is very difficult to solve its singular integral. In this paper, we propose a Hermite cubic spline multi-wavelet natural boundary element method. The Hermite cubic spline multi-wavelet has shorter tight collection, better stability and good explicit expression. Moreover, their derivatives on different levels are mutual orthogonal. Accordingly, taking advantage of Galerkin-wavelet method in discretizing the natural boundary integral equation and integral of the natural boundary element method with the above-mentioned, this paper makes the strongly singular integral of the natural boundary equations change into the weakly singular integral, so the problem is simplified. A numerical example is shown and the feasibility and validity of the method are proved.