Numerical solution of hypersingular equation using recursive wavelet on invariant set

In this paper, we construct the Chebyshev recursive wavelets on a unit interval of the first kind, the second kind and their corresponding weight functions. We apply wavelet collocation method to solve the natural boundary integral equation of the harmonic equation on the lower half-plane numerically. It is convenient and accurate to generate the stiffness matrix. Two numerical examples are presented. It is shown that the stiffness matrix is highly sparse when the order of the stiffness matrix becomes large. Current method allows choosing an appropriate weight function to increase the convergence rate and accuracy of the numerical results.