A new modified nonstandard finite difference method for solving one-dimensional autonomous differential equations is constructed and analyzed. It is based on the theta method and is both elementary stable and of second-order accuracy. A set of numerical simulations is also presented that supports the theoretical results.

中文翻译：

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一维自治微分方程的二阶修正非标准theta方法

构造并分析了一种新的改进的非标准有限差分方法，用于求解一维自治微分方程。它基于theta方法，既基本稳定又具有二阶精度。还提供了一组数值模拟来支持理论结果。