In the present paper, we formulate a generalized family of symmetric multistep methods (GFSMMs) for solving initial value problems in ordinary differential equations. Future solution values are inherent in the GFSMMs. However, a purely interpolatory approach is applied for the derivation of the GFSMMs and a detailed theoretical and computational study is presented. These include the order, stability, interval of periodicity, and phase-lag (PL) analysis of the methods. Some of the proposed methods herein possess minimal PL error constants, while some have high-order PL. Also, some of the proposed GFSMMs are P-stable, while some exhibit multiple intervals of periodicity. The application of the newly formulated schemes are demonstrated in the numerical experiments presented.

中文翻译：

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常微分方程初值问题的具有最小相位滞后的广义对称多步方法族

在本文中，我们制定了一套广义的对称多步方法（GFSMM），用于解决常微分方程中的初值问题。GFSMM中固有的是将来的解决方案值。但是，纯插值方法适用于GFSMM的推导，并提供了详细的理论和计算研究。这些包括方法的顺序，稳定性，周期性间隔和相位滞后（PL）分析。本文提出的一些方法具有最小的PL误差常数，而某些方法具有高阶PL。同样，一些提出的GFSMM是P稳定的，而有些则表现出多个周期性间隔。提出的数值实验证明了新制定的方案的应用。