多步Runge－Kutta方法的收敛阶

THE ORDER OF CONVERGENCE OF MULTISTEP RUNGE-KUTTA METHODS

本文讨论了代数稳定的多步Ｒｕｎｇｅ－Ｋｕｔｔａ方法求解常微分方程初值问题时可达到的收剑阶．所获阶结果为Ｒｕｎｇｅ—Ｋｕｔｔａ方法的相应结果的推广．

In this paper we present some order properties of algebraically stable multistep Runge-Kutta methods for solving initial valuo problems in ordinary differential equations. The order results for multistep Runge-Kutta methods obtained in this paper extend those obtained by Butcher[5], Burrage[1], Burrage and Chipman[3],and Wanner and Hairer[4],and can be regarded as a extension of the well known order results for Runge-Kutta methods.