Fixed Point Analytical Method for Nonlinear Differential Equations

被引:5
|
作者
Xu, Ding [1 ]
Guo, Xin [2 ]
机构
[1] Xi An Jiao Tong Univ, Sch Aerosp, State Key Lab Strength & Vibrat Mech Struct, Xian 710049, Peoples R China
[2] Coal Technol & Engn Grp Corp, Xian Res Inst China, Xian 710054, Peoples R China
来源
基金
中国国家自然科学基金;
关键词
fixed point analytical methods; uniform validity; nonlinear equation; perturbation;
D O I
10.1115/1.4006337
中图分类号
TH [机械、仪表工业];
学科分类号
0802 ;
摘要
In this paper, a new analytical method, which is based on the fixed point concept in functional analysis (namely, the fixed point analytical method (FPM)), is proposed to acquire the explicit analytical solutions of nonlinear differential equations. The key idea of this approach is to construct a contractive map which replaces the nonlinear differential equation into a series of linear differential equations. Usually, the series of linear equations can be solved relatively easily and have explicit analytical solutions. The FPM is different from all existing analytical methods, such as the well-known perturbation technique applied in weakly nonlinear problems, because it is independent of any small physical or artificial parameters at all; thus, it can handle more nonlinear problems, including strongly nonlinear ones. Two typical cases are investigated by FPM in detail and the comparison with the numerical results shows that the present method is one of high accuracy and efficiency. [DOI: 10.1115/1.4006337]
引用
收藏
页数:9
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