Approximate analytical solutions for a class of nonlinear differential equations

Zheng Lian-Cun; Feng Zhi-Feng; Zhang Xin-Xin

doi:10.7498/aps.56.1549

Abstract
This paper presents a theoretical analysis for a class of generalized diffusion equations. An effective analytical decomposition and numerical technique is given by similarity transformations and the analytical decomposition technique. The approximate analytical solution may be expressed in terms of a rapid convergent power series with elegantly computable terms. The reliability and efficiency of approximate solutions are illustrated by good agreement with numerical results.

Keywords:
diffusion equations /

nonlinear boundary value problems /

analytical decomposition /

approximate solution
Authors and contacts
Zheng Lian-Cun²,

Feng Zhi-Feng²,

Zhang Xin-Xin¹

(1)北京科技大学机械工程学院,北京 100083; (2)北京科技大学数学力学系，北京 100083
References

Cited By

[1]	Li Yong-Qiang, Liu Ling. A study of capillary flow in variable interior corners under microgravity. Acta Physica Sinica, 2014, 63(21): 214704. doi: 10.7498/aps.63.214704
[2]	Lu Fa-Lin, Chen Chang-Yuan, You Yuan. Approximate analytical solutions of bound states for the double ring-shaped Hulthn potential. Acta Physica Sinica, 2013, 62(20): 200301. doi: 10.7498/aps.62.200301
[3]	Shen Yong-Jun, Yang Shao-Pu, Xing Hai-Jun. Dynamical analysis of linear single degree-of-freedom oscillator with fractional-order derivative. Acta Physica Sinica, 2012, 61(11): 110505. doi: 10.7498/aps.61.110505
[4]	Shen Yong-Jun, Yang Shao-Pu, Xing Hai-Jun. Dynamical analysis of linear SDOF oscillator with fractional-order derivative (Ⅱ). Acta Physica Sinica, 2012, 61(15): 150503. doi: 10.7498/aps.61.150503
[5]	Mo Jia-Qi, Chen Xian-Feng. Approximate solution of solitary wave for a class of generalized nonlinear disturbed dispersive equation. Acta Physica Sinica, 2010, 59(3): 1403-1408. doi: 10.7498/aps.59.1403
[6]	Mo Jia-Qi, Chen Xian-Feng. Approximate analytic solution of solitary wave for a class of nonlinear disturbed Nizhnik-Novikov-Veselov system. Acta Physica Sinica, 2010, 59(5): 2919-2923. doi: 10.7498/aps.59.2919
[7]	Yang Pei, Chen Yong, Li Zhi-Bin. Analytic approximation for the soliton solution of the discrete modified KdV equation. Acta Physica Sinica, 2010, 59(6): 3668-3673. doi: 10.7498/aps.59.3668
[8]	Hu Xian-Quan, Cui Li-Peng, Luo Guang, Ma Yan. The analytic solution of the radial Schr?dinger equation for the superposed potentials. Acta Physica Sinica, 2009, 58(4): 2168-2173. doi: 10.7498/aps.58.2168
[9]	Mo Jia-Qi. Analytic solution for a class of generalized Sine-Gordon perturbation equation. Acta Physica Sinica, 2009, 58(5): 2930-2933. doi: 10.7498/aps.58.2930
[10]	Hou Dong-Xiao, Liu Bin, Shi Pei-Ming. The bifurcation of a kind of relative rotational dynamic equation with hysteresis and its approximate solution. Acta Physica Sinica, 2009, 58(9): 5942-5949. doi: 10.7498/aps.58.5942
[11]	Mo Jia-Qi. Approximate analytic solution to a class of generalized Canard systems. Acta Physica Sinica, 2009, 58(2): 695-698. doi: 10.7498/aps.58.695
[12]	Shi Lan-Fang, Mo Jia-Qi. Soliton-like homotopic approximate analytic solution for a class of disturbed nonlinear evolution equation. Acta Physica Sinica, 2009, 58(12): 8123-8126. doi: 10.7498/aps.58.8123
[13]	Zhang Yan, Zheng Lian-Cun, Zhang Xin-Xin. The analytical approximate solution for Marangoni convection in a liquid layer with coupled boundary conditions. Acta Physica Sinica, 2009, 58(8): 5501-5506. doi: 10.7498/aps.58.5501
[14]	Wei Gao-Feng, Long Chao-Yun, Qin Shui-Jie, Zhang Xin. Analytical approximations to the arbitrary l-wave bound state solutions of the Klein-Gordon equation for the Manning-Rosen potential. Acta Physica Sinica, 2008, 57(11): 6730-6735. doi: 10.7498/aps.57.6730
[15]	Mo Jia-Qi, Wang Hui, Lin Wan-Tao. Approximate analytic solution of land-air couplind dynamical system. Acta Physica Sinica, 2006, 55(2): 485-489. doi: 10.7498/aps.55.485
[16]	Zheng Lian-Cun, Sheng Xiao-Yan, Zhang Xin-Xin. Analytical approximate solutions for Marangoni convection boundary layer equations. Acta Physica Sinica, 2006, 55(10): 5298-5304. doi: 10.7498/aps.55.5298
[17]	Xie Yuan-Xi, Tang Jia-Shi. A note on paper “a simple fast method in finding the analytical solutions to a class of nonlinear partial differential equations”. Acta Physica Sinica, 2005, 54(3): 1036-1038. doi: 10.7498/aps.54.1036
[18]	Xie Yuan-Xi, Tang Jia-Shi. A simple fast method in finding the analytical solutions to a class of nonlinear partial differential equations. Acta Physica Sinica, 2004, 53(9): 2828-2830. doi: 10.7498/aps.53.2828
[19]	Zhang Shan-Qing, Li Zhi-Bin. . Acta Physica Sinica, 2002, 51(10): 2197-2201. doi: 10.7498/aps.51.2197
[20]	LI ZHI-BIN, YAO RUO-XIA. EXPLICIT EXACT SOLUTIONS TO NONLINEARCOUPLED DIFFERENTIAL EQUATIONS. Acta Physica Sinica, 2001, 50(11): 2062-2067. doi: 10.7498/aps.50.2062

Catalog

Vol. 56, Issue 3 - 2007-02-05

Metrics

Abstract views: 9389
PDF Downloads: 2052
Cited By: 0

姓名
邮箱
手机号码
标题
留言内容
验证码

Search

Article

留言板

Approximate analytical solutions for a class of nonlinear differential equations

Abstract

Authors and contacts

References

Cited By

Catalog

Metrics

Authors

Referees

About Journal

About

Search

Article

留言板

Approximate analytical solutions for a class of nonlinear differential equations

Abstract

Authors and contacts

References

Cited By

Catalog

Metrics

Publishing process

Authors

Referees

About Journal

About