一种新的常微分方程数值方法构建思路及公式构建与分析

A New Construction Idea for ODE Numerical Method and Construction and Analysis of Related Formulas

提出一种新的常微分方程数值方法的构建思路,构建相关公式并分析其稳定性,通过实例检验新方法的计算精度.按照新思路提出的算法公式具有以下特点:形式繁多,既可以构建显式方法,也可以构建隐式方法;稳定性好,新算法对实验方程具有很好的稳定性;计算精度高,公式计算精度高于传统的四阶公式.因此,提出的新方法具有实用价值.

A new construction idea for ordinary differential equation（ODE）numerical method was raised,some related formulas were set up and their stability were analyzed.The calculation accuracy of the new method was verified by an example.The numerical method constructed according to the idea have the following characteristics：the formulas have various forms which can construct both explicit and implicit methods,there is a good stability to the experimental equation and calculation accuracy of new formulas are higher than the traditional four order formula.Thus,the new method proposed has practical value.