弹性降阶变换及其在求解一类三阶非线性微分方程中的应用  

On the Elastic Descending Order Transformation and Its Application in Solving a Class of Third-order Nonlinear Differential Equation

作　　者：李顺初 刘盼 邵东凤 付雪倩 范林 桂钦民 LI Shunchu;LIU Pan;SHAO Dongfeng;FU Xueqian;FAN Lin;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1期1-5,共5页Journal of Xuzhou Institute of Technology(Natural Sciences Edition)

摘　　要：弹性在经济学和工程科学中均有重要理论与实用价值,该文根据弹性的特征,创新性地引入了一种微分变换——弹性降阶变换.通过弹性降阶变换可将一类三阶非线性微分方程化为第二种Weber方程,从而获得此三阶非线性微分方程的解析解.正如积分变换中的傅里叶变换在频谱分析的重要地位,研究了作为微分变换的弹性变换在求解微分方程中的重要作用.该研究成果对扩大非线性微分方程的可解类具有重要意义,为微分方程的求解提供了一个新的思路.Elasticity has important theoretical and practical value in economics and engineering science.According to the characteristics of elasticity,this paper innovatively introduces a differential transformation i.e.elastic descending order transformation,which can be used to transform a class of third-order nonlinear differential equations into the second Weber equation,and the analytical solution of the third-order nonlinear differential equation can be obtained.The important role of the elastic transform as differential transform in solving differential equations is studied in this paper,which is as important as Fourier transform in spectrum analysis.Therefore,the research results are of great significance for expanding the solvable class of differential equations with a new thinking method.

关 键 词：非线性微分方程 第二种weber方程 弹性 弹性降阶变换 

分 类 号：O175.1[理学—数学]