April 2023 ELASTIC TRANSFORMATION AND ITS INVERSE TRANSFORMATION FOR SOLVING FIRST- AND THIRD-ORDER NONLINEAR VARIABLE COEFFICIENT ORDINARY DIFFERENTIAL EQUATIONS
Xiaoxu Dong, Qun Liu, Wenjing Li, Zheng Zeng, Shunchu Li, Xing Xia
Rocky Mountain J. Math. 53(2): 417-434 (April 2023). DOI: 10.1216/rmj.2023.53.417

Abstract

Here elastic transformation and its inverse transformation are used to solve two kinds of first- and third-order nonlinear ordinary differential equations (ODEs) with variable coefficients. First, elastic transformations are used to upgrade and reduce the first- and third-order nonlinear ODEs to a class of second-order linear homogeneous ODEs. Then the general solutions of the first- and third-order ODEs are obtained separately by using the general solution of the obtained second-order linear homogeneous ODEs, elastic transformation, inverse transformation of elastic transformation and related operation rules. Second, the steps for solving these two kinds of ODEs are summarized. Finally, examples and parametric analysis are given to prove that it is effective, simple and feasible to solve two kinds of first- and third-order nonlinear ODEs by elastic transformation and its inverse transformation. Elastic transformation and its inverse transformation provide a new method for solving ODEs. The research in this paper expands the solvable classes of ODEs.

Citation

Download Citation

Xiaoxu Dong. Qun Liu. Wenjing Li. Zheng Zeng. Shunchu Li. Xing Xia. "ELASTIC TRANSFORMATION AND ITS INVERSE TRANSFORMATION FOR SOLVING FIRST- AND THIRD-ORDER NONLINEAR VARIABLE COEFFICIENT ORDINARY DIFFERENTIAL EQUATIONS." Rocky Mountain J. Math. 53 (2) 417 - 434, April 2023. https://doi.org/10.1216/rmj.2023.53.417

Information

Received: 29 March 2022; Revised: 17 April 2022; Accepted: 12 May 2022; Published: April 2023
First available in Project Euclid: 20 June 2023

MathSciNet: MR4604764
zbMATH: 07725145
Digital Object Identifier: 10.1216/rmj.2023.53.417

Subjects:
Primary: 34A05 , 34A34

Keywords: elastic transformation method , general solution , inverse transform of elastic transform , nonlinear , ODE with variable coefficients

Rights: Copyright © 2023 Rocky Mountain Mathematics Consortium

JOURNAL ARTICLE
18 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

Vol.53 • No. 2 • April 2023
Back to Top