摘要
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.
作者
孟纯青
MENG Chunqing(College of Film and TV,Shanghai Theatre Academy,Shanghai 200040,Chin)
出处
《上海工程技术大学学报》
CAS
2018年第2期162-168,共7页
Journal of Shanghai University of Engineering Science
关键词
常微分方程数值方法
加权平均公式
预估校正公式
稳定性
numerical method for ordinary differential equation （ODE）
weighted average formula
predictor-corrector formula
stability
