标题： 常微分方程的变步长SDIMSIMs 显示英文标题

标题： Variable stepsize SDIMSIMs for ordinary differential equations

摘要： 二阶导数通用线性方法（SGLMs）已经在使用Nordsieck技术的可变步长环境中实现。 在本文中，我们直接在非均匀网格上引入可变步长SGLMs。 通过推导所提出方法的阶条件，阶为$p$且阶段阶为$q=p$，给出了一些这些方法到四阶的显式示例。 通过一些数值实验，我们展示了所提出方法在求解非刚性问题中的效率，并确认了理论上的收敛阶。 显示英文摘要

摘要： Second derivative general linear methods (SGLMs) have been already implemented in a variable stepsize environment using Nordsieck technique. In this paper, we introduce variable stepsize SGLMs directly on nonuniform grid. By deriving the order conditions of the proposed methods of order $p$ and stage order $q=p$, some explicit examples of these methods up to order four are given. By some numerical experiments, we show the efficiency of the proposed methods in solving nonstiff problems and confirm the theoretical order of convergence.