Projection methods for a class of Hammerstein equations

Here some new convergence results for a class of Hammerstein equations are given. A particular example, appearing in the solution of a steady-state heat conduction problem with a nonlinear boundary condition, was recently studied by Ruotsalainen and Wendland [Numer. Math., 53 (1988), pp. 299–314], using the Galerkin approximation and by Ruotsalainen and Saranen [JCAM, 28 (1989), pp. 339–348], using collocation. This paper improves the convergence results in both of these works. The general result also applies to some time-dependent nonlinear model problems.