Numerical method for a nonlinear boundary integral equation

We study a boundary integral equation method for solving Laplace’s equation Δu = 0 with nonlinear boundary conditions. This nonlinear boundary value problem is reformulated as a nonlinear boundary integral equation, with u on the boundary as the solution being sought. The integral equation is solved numerically by using the Wavelet–Galerkin method, with Legendre wavelet functions used as approximations to u. numerical example are given for problem.