%0 Journal Article
%T 常微分方程初值问题的区域分解逼近方法<br>Domain Decomposition Approximation of Initial Value Problems for Ordinary Differential Equations
%A 宋灵杉
%A 梁同洋
%A 刘工业
%J Advances in Applied Mathematics
%P 228-237
%@ 2324-8009
%D 2025
%I Hans Publishing
%R 10.12677/aam.2025.145251
%X 本文主要借助拉格朗日插值逼近来求解常微分方程初值问题的近似解&#65292;利用插值基函数展开数值解&#65292;将问题转化为线性或非线性方程组&#65292;对非线性方程组采用不动点迭代法求解。数值实验表明&#65292;多区域方法比单区域方法误差更小。<br>This article mainly uses Lagrangian interpolation approximation to solve the approximation solution of the initial value problem of ordinary differential equations. The numerical solution is expanded by using interpolation basis functions, and the problem is transformed into a system of linear or nonlinear equations. The fixed-point iteration method is used to solve the system of nonlinear equations. Numerical experiments show that the multi-domain method has a smaller error than the single-region method.
%K 常微分方程&#65292
%K 初值问题&#65292
%K 拉格朗日插值法&#65292
%K 多区域配置法<br>Ordinary Differential Equations
%K Initial Value Problem
%K Lagrange Interpolation Method
%K Collocation of Multi-Domain
%U http://www.hanspub.org/journal/PaperInformation.aspx?PaperID=115057