高阶非线性常微分方程边值问题的Lagrange插值逼近

Lagrange Interpolation Approximation for Edge Value Problems of Higher-Order Nonlinear Ordinary Differential Equations

摘要: 本文通过选取等距节点为插值节点，利用Lagrange插值的微分矩阵，对高阶非线性常微分方程进行Lagrange插值逼近，最终转化为求解非线性方程组问题，利用不动点迭代法进行求解，并计算与解析解的误差的数量级来说明此方法的精确性，此方法对求解高阶非线性常微分方程具有重要意义。

Abstract: In this paper, equidistant nodes are selected as interpolation nodes, and the differential matrix of Lagrange interpolation is used to approximate the high-order nonlinear ordinary differential equa-tion, which is finally transformed into solving the problem of nonlinear equations. The fixed point iteration method is used to solve the problem, and the order of error between the calculation and analytical solution is calculated to illustrate the accuracy of this method. This method is of great significance to solving high-order nonlinear ordinary differential equations.