On the collocation method for a nonlinear boundary integral equation

摘要

In this paper we study a potential problem with a nonlinear boundary condition. Using the Green representation formula for a harmonic function we reformulate the nonlinear boundary value problem as a nonlinear boundary integral equation. We shall give a brief discussion of the solvability of the integral equation. The aim of this paper, however, is to analyse the collocation method for finding an approximate solution to this equation. Using the theory of a-proper and a-stable mappings we prove the unique solvability of the collocation equations and the asymptotic error estimates. To do this we assume that the nonlinearity is strongly monotone.