关于数值求解常微分方程的二阶导数方法的最高可达阶及其Stiff稳定性

On the Attainable Highest Order and Stiffly Stability of Second Derivative Methods for Numerical Solution of Ordinary Differential Equations

本文讨论了具有一般形式的二阶导数方法的最高可达阶及其稳定性。论证了零稳定的二阶导数方法的最高可达阶是2K＋2。

In this paper, we discuss the attainable order and stability of the second derivative methods in the general form sum from i=0 to K α_iy_(n+i)=h sum from i=0 to K β_iy′_(n+i)+h^2 sum from i=0 to K γ_iy″_(n+i). We have demonstrated that the attainable highest order of zero-stable second derivative methods is 2K+2, and stiffly stable second derivative methods is 2K+1.