An implicit numerical spline method for systems for ODEs

摘要

An implicit numerical method is introduced that gives piecewise polynomial spline approximations for the solution of an initial value problem for the equationy′(t)=f(t,y(t)).Here, f is a function having continuous derivatives up to the order r. The method presented in this work, provides spline functions which approximate the solution of the problem in the most regular function space Cr+1. Error estimates in C and Cr+1 are given and the stability of the method is investigated.