L�sung von Differentialgleichungen mit Splinefunktionen. Eine St�rungstheorie

Abstract

In this paper non-linear splines (depending onn+1 parameters) are used to patch up the solution of an initial value problem in intervals of stepsizeh. The elements of the solution are fixed byq smoothness conditions andd conditions derived from the differential equation in an appropriate setup. The feasibility of the method can be connected to that of the polynomial spline method by a perturbation type argument. Thus the question of convergence forh→0 is closely connected to the linear (polynomial) case.