Splineapproximationen von beliebigem Defekt zur numerischen Lösung gewöhnlicher Differentialgleichungen. Teil III

Summary In the first part 1] a general procedure is presented to obtain polynomial spline approximations for the solutions of initial value problems for ordinary differential equations; furthermore a divergence theorem is proved there. Sufficient conditions for convergence of the method are given in the second part 2]. The remaining case which has not been considered in 1] and 2] is treated in the present paper. In this special case the procedure is equivalent to an unstable two-step method with special initial values; nevertheless, convergence can be proved. Finally,A ₀-stability of the method as well as the influence of rounding errors are investigated.