一类典型二阶非线性微分方程的近似解析解研究  

A study of approximate analytical solutions of a kind of typical second-order nonlinear different equation

作　　者：楼智美[1] 王元斌[2] 王鹏[3] LOU Zhi-mei;WANG Yuan-bin;WANG Peng(Department of Physics,Shaoxing University,Shaoxing Zhejiang 312000,China;Department of Mathematics,Shaoxing University,Shaoxing Zhejiang 312000,China;School of Civil Engineering and Architecturv,University of dinah,dinah 250022,China)

机构地区：[1]绍兴文理学院物理系,浙江绍兴312000 [2]绍兴文理学院数学系,浙江绍兴312000 [3]济南大学土建学院,济南250022

出　　处：《华东师范大学学报（自然科学版）》2018年第4期129-137,共9页Journal of East China Normal University(Natural Science)

基　　金：国家自然科学基金(11472177;11772141)

摘　　要：在非惯性转动参照系中研究力学体系的运动,常常会出现一类分子分母都含非线性项的二阶非线性微分方程,很难求得其近似解.用Adomian分解法研究了这类典型二阶非线性微分方程的近似解,在给定的初始条件和参数下得到了近似解的解析表达式,并作出了近似解析解的解曲线;与直接用Mathematica软件得到的数值解曲线和用同伦渐近法得到的近似解析解曲线进行了比较,结果表明,在第一个1/4周期时间内,用Adomian分解法得到的近似解解曲线与直接用Mathematica软件得到的数值解曲线十分吻合,并且其误差比用同伦渐近法得到的解曲线更小.In a non-inertial rotational reference frame,the motion of a system can be governed by a kind of second-order nonlinear differential equation,in which the numerator and denominator both contain nonlinear terms; in this context,it is hard to obtain an approximate solution for this strongly nonlinear equation.In this paper,we study the approximate solution of the second-order nonlinear differential equation by the Adomian decomposition method.Comparisons between the approximate solution and the numerical solution by using two other methods are also made.The results show that,in the first quarter period,the approximate solutions obtained by the Adomian decomposition method is in good agreement with the numerical solutions and the error of the approximate solutions are smaller than the other solutions obtained by the homotopy asymptotic method.

关 键 词：ADOMIAN分解法 二阶非线性微分方程 近似解析解 数值解 

分 类 号：O316[理学—一般力学与力学基础]