基于弹性降阶变换法求解一类可化为Legendre方程的微分方程初值问题  

Solving the Initial Value Problem of a Class of Differential Equations Transformed into Legendre Equations on the Basis of Elastic Descending Order Transformation Method

作　　者：李顺初 邵东凤 范林 刘盼 付雪倩 桂钦民 LI Shunchu;SHAO Dongfeng;FAN Lin;LIU Pan;FU Xueqian;GUI Qinmin(School of Science,Xihua University,Chengdu 610039,China;Beijing Dongrunke Petroleum Technology It discusses,Beijing 100029,China)

机构地区：[1]西华大学理学院,四川成都610039 [2]北京东润科石油技术股份有限公司,北京100029

出　　处：《徐州工程学院学报（自然科学版）》2022年第4期1-7,共7页Journal of Xuzhou Institute of Technology(Natural Sciences Edition)

基　　金：西华大学校人才引进项目(Z201076)。

摘　　要：针对一类三阶非线性常微分方程初值问题,根据弹性的微分性质引入一种新的弹性降阶变换法.论述了其引入背景和求解步骤,揭示了该方法的本质特征:只要通过弹性降阶变换法转化后的微分方程可解,那么原微分方程初值问题也是可解的.弹性降阶变换法可转化为Legendre方程初值问题的一类三阶非线性常微分方程初值问题进行求解,不仅扩大了微分方程的可解类,还为微分方程的研究提供了新的思想方法.Aiming at the initial value problem of a class of third-order nonlinear ordinary differential equations, this paper introduces a new transformation method, i.e. lastic descending order transformation method according to the differential properties of elasticity Co.,Ltd., discusses its introduction background and solving steps, and reveals the essential characteristics of this method: as long as the differential equation transformed by elastic descending order transformation method is solvable, the initial value problem of the original differential equation is also solvable. In this paper, the initial value problem of a class of third-order nonlinear ordinary differential equation that can be transformed into Legendre equation initial value problem by elastic decending order transformation method is solved. This method not only enlarges the solvable class of differential equations, but also provides a new thinking method for the study of differential equations.

关 键 词：微分方程 非线性 Legendre方程 弹性降阶变换法 初值问题 

分 类 号：O175.1[理学—数学]