Semianalytic Discretization of Weakly Nonlinear Boundary Value Problems with Variable Coefficients

Abstract

A new technique for the iterative treatment of two-point boundary value problems by means of piecewise simplified operators is investigated. Unlike in previous approaches the main part of the differential operator is also used in the projected right hand side of the recursion of the Iteration process. We show the iterates recursively to be piecewise smooth enough to prove the contractivity of the mapping of the iteration. We state the local convergence of the discretization with respect to the step size of the underlying grid.