基于弹性升阶变换求解一类可化第一种Weber方程的微分方程初值问题  

Elastic Ascending Order Transformation Method for Solving the Initial Value Problem of a Class of Differential Equation Transformed into the First Weber Equation

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 Co,Ltd.,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）》2023年第3期9-14,共6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：对于非线性常微分方程初值问题的求解,并没有一般化的求解方法,于是根据弹性的特性引入了一种新的微分变换-弹性升阶变换.针对一类一阶非线性常微分方程的初值问题,通过弹性升阶变换,把它转化成第一种Weber方程的初值问题,从而获得其解.弹性升阶变换的应用不仅扩大了微分方程的可解类,而且为微分方程初值问题的求解提供了新思路.There is no general solution to the initial value problem of nonlinear ordinary differential equations.Therefore,this paper introduces a new differential transformation-elastic ascending transformation according to the characteristics of elasticity.For the initial value problem of a class of first-order nonlinear ordinary differential equations,the solution can be obtained by transforming it into the initial value problem of the first Weber equation through the elastic ascending transformation.The application of elastic ascending transformation not only expands the solvable class of differential equations,but also provides new ideas for solving the initial value problems of differential equations.

关 键 词：微分方程 非线性 第一种Weber方程 弹性升阶变换 初值问题 

分 类 号：O175.1[理学—数学]