常微分方程组初值问题的Lagrange插值逼近方法  

Lagrange Interpolation Approximation Method for Initial Value Problems of Ordinary Differential Equations

作　　者：万广霞 杨浩文 

机构地区：[1]河南科技大学数学与统计学院,河南 洛阳

出　　处：《应用数学进展》2024年第5期2358-2365,共8页Advances in Applied Mathematics

摘　　要：常微分方程的快速发展和很多学科有着紧密的关系,随着众多的数学家对其研究的不断加深,极大地推动了现代数学的发展。因此,本文研究拉格朗日插值(Lagrange)逼近方法在常微分方程组初值问题上的应用,推导出Lagrange插值法的逼近算法,求解常微分方程组初值问题的数值解,也就是通过具体的例子,利用Lagrange插值逼近方法构造相对应的数值格式,寻找误差和多项式次数的关系,将结果可视化,最后对相应的误差结果进行分析。数值结果表明Lagrange插值逼近方法具有较高的精度。The rapid development of ordinary differential equations is closely related to many disciplines, and with the continuous deepening of the research of many mathematicians, the development of modern mathematics has been greatly promoted. Therefore, this paper studies the application of the Lagrange interpolation approximation method in the initial value problem of ordinary differential equations, deduces the approximation algorithm of the Lagrange interpolation approximation method, and solves the numerical solution of the initial value problem of ordinary differential equations. The numerical results show that the Lagrange interpolation approximation method has high accuracy.

关 键 词：常微分方程组 初值问题 Lagrange插值逼近 等距节点 

分 类 号：O17[理学—数学]