常微分方程的多区域配置方法

A Multi-Domain Collocation Method of Ordinary Differential Equations

摘要: 以等距节点为插值节点，构造常微分方程的Lagrange插值逼近算法格式，将常微分方程转化成矩阵方程求解。通过将区域分解的方式提高算法精度，数值实验证明本文所提算法的高精度，此方法可以广泛应用到其他常微分方程的求解中。

Abstract: Using equidistant nodes as interpolation nodes, construct a Lagrange interpolation approximation algorithm format for ordinary differential equations, and transform the ordinary differential equations into matrix equations for solution. By decomposing regions, the algorithm accuracy is improved, and numerical experiments have demonstrated the high accuracy of the proposed algorithm. This method can be widely applied to the solution of other ordinary differential equations.