一类微分方程的数值解法误差分析  

Error Analysis of Numerical Solution for A Class of Differential Equations

作　　者：王祝园 沈进 WANG Zhu-Yuan;SHEN Jin(School of General Courses,Anhui Medical College,Hefei Anhui 230601;Basic Department,An Hui San Lian University,Hefei 230601)

机构地区：[1]安徽医学高等专科学校公共基础学院,安徽230601 [2]安徽三联学院基础部,安徽230601

出　　处：《佳木斯大学学报（自然科学版）》2024年第11期177-180,共4页Journal of Jiamusi University：Natural Science Edition

基　　金：安徽省教育厅重点科研项目(KJ2021A1185)。

摘　　要：含初值问题的微分方程广泛应用于实际生活中的多个领域,其数值解法的误差分析尤为重要.本文提出了一类初值问题的微分方程为一阶同型微分方程,针对同型微分方程,利用欧拉公式法和改进的欧拉公式法探讨了利普西茨常数及不同的步长对整体误差的分析,并用实例进行了说明.Differential equations with initial value problems are widely used in many fields in real life,and the error analysis of their numerical solutions is particularly important.In this paper,it is proposed a class of differential equation of initial value problems are defined first-order homomoraphic differential equations.For the homomoraphic differential equations,the analysis of Lipschitz constant and different step lengths on the overall error are discussed by using the Euler formula method and the improved Euler formula method,and some examples are given to illustrate them.

关 键 词：同型微分方程 初值问题 利普西茨常数 误差分析 

分 类 号：O241[理学—计算数学]