Stronger than uniform convergence of multistep difference methods

Abstract

This paper is concerned with the numerical integration of ordinary differential equations of the order x. Sufficient conditions and also necessary ones are given for the s-th difference quotient of the approximate solution to approach the s-th derivative of the exact solution for s >0. This requires a more subtle examination of the multiplicities of the characteristic roots of modulus 1. © 1966 Springer-Verlag.