High Accuracy Mechanical Quadrature Method For Solving Nonlinear Boundary Integral Equations

This paper presents mechanical quadrature methods for solving the boundary integral equations of nonlinear boundary value problems. After the boundary integral operator is decomposed into the sum of a monotonous Hammerstein operator and a compact mapping by the Sidi rule, we construct the nonlinear discrete equations. Using the asymptotically compact theory of Anselone' and Stepleman' theorem, the existence, the unicity , the convergence and the error estimate with O(h3) of the discrete equations are shown. By fixed-point arguments of Ostrowski, a modified Newton iteration with the third order is presented. Numerical examples show that our methods are effective.