Stationary and nonstationary iterative methods for nonlinear boundary value problems

Abstract

For a given differential system together with nonlinear boundary conditions, we develop a very general class of stationary and nonstationary iterative methods. Assuming the existence of a continuous approximate solution of the problem, we provide sufficient conditions for the convergence of these iterative methods. The computational aspects of these iterative methods are also discussed. Further, to make the analysis widely applicable, all the results are proved component-wise. © 1993.