The numerical approximation of the solution of a nonlinear boundary integral equation with the collocation method (Q1188404)

Using an easily computable \(L^ 2\)-orthogonal projection of the nonlinear function, the authors propose an approximation scheme for the nonlinear boundary integral equation which arises in solving the potential problem with a nonlinear boundary condition. For simplicity this approach applies to collocation methods only. It turns out that this collocation scheme preserves the theoretical \(L^ 2\)- convergence. Numerical experiments confirm their theoretical results.