线性微分方程的有限差分法求解周期正解  

Finite Difference Method of Linear Differential Equations to Solve Periodic Positive Solution

作　　者：何洋 HE Yang(Foundational Department,Chuzhou City Vocational College,Chuzhou 239000,China)

机构地区：[1]滁州城市职业学院基础部,安徽滁州239000

出　　处：《长春大学学报》2023年第2期38-43,共6页Journal of Changchun University

基　　金：安徽省教育厅重点项目(SK2019A1092);安徽省职业与成人教育学会重点课题(AGZ18001,azcg162)。

摘　　要：为了提高线性微分方程在求解计算中的性能,提出了线性微分方程的有限差分法求解周期正解。证明了线性微分方程的有限差分格式与能量守恒的离散规则是等价关系,分析了线性微分方程差分格式的正性和周期性,实现了基于有限差分法的线性微分方程求解周期正解。最后通过数值实验的方式,得出与传统差分法求解线性微分方程的周期正解相比,不仅满足了正性要求,还满足了周期性要求。In order to improve the performance of linear differential equations in solution calculation,a finite difference method of linear differential equations to solve periodic positive solutions is proposed.It is proved that the finite difference scheme of linear differential equations is equivalent to the discrete rule of energy conservation,the positive property and periodicity of the difference scheme of linear differential equations are analyzed,and the periodic positive solution of linear differential equations based on finite difference method is realized.Finally,the results of numerical experiments show that,compared with the traditional difference method for solving the periodic positive solutions of linear differential equations,it not only meets the positive requirements,but also meets the periodic requirements.

关 键 词：有限差分法 线性微分方程 哈密尔顿系统 求解 

分 类 号：O241.82[理学—计算数学]