Abstract We introduce second derivative two-step collocation methods for the numerical integration of ordinary differential equations. In these methods, the solution of the problem in each step depends on the numerical solution in some points in the two previous steps. These methods are obtained using the collocation approach by relaxing some of the collocation conditions to obtain methods with desirable stability properties. The construction technique, analysis of the order of accuracy and linear stability properties of the methods are described.

中文翻译：

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常微分方程的二阶导数两步搭配法

摘要 我们介绍了常微分方程数值积分的二阶导数两步配置方法。在这些方法中，每一步问题的解都依赖于前两步中某些点的数值解。这些方法是使用搭配方法通过放宽一些搭配条件获得的，以获得具有所需稳定性的方法。描述了构造技术、精度阶数分析和方法的线性稳定性特性。