EXACT SOLUTIONS OF TWO CLASSES OF SECOND ORDER NONLINEAR ORDINARY DIFFERENTIAL EQUATIONS WITH THE CONTACT STRUCTURE

被引：0

作者：

Wang, Kaizhi ^{[1
]}

Zhong, Tingyu ^{[1
]}

机构：

[1] Shanghai Jiao Tong Univ, Sch Math Sci, Shanghai 200240, Peoples R China

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S | 2025年

基金：

上海市自然科学基金;

关键词：

Convergence; Lie<acute accent>nard equation; parachute equation; exact solution; EXPLICIT EXACT-SOLUTIONS; VARIATIONAL ITERATION; LIENARD EQUATION;

D O I：

10.3934/dcdss.2025011

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We use an iteration method to obtain exact solutions of two classes of nonlinear ordinary differential equations with the contact structure-Lie<acute accent>nard equations and parachute equations. Our analysis establishes the uniform convergence of the iterative sequence to the exact solutions of the equations on some closed interval, thereby offering a way to finding exact solutions to the equations. As applications, we apply the main results to two examples with physical interests, the Van der Pol equation and the parachute equation, alongside the presentation of some numerical results.

引用

页数：20