New homotopy analysis transform method for solving the discontinued problems arising in nanotechnology

doi:10.1088/1674-1056/22/11/110201

Abstract We present a new reliable analytical study for solving the discontinued problems arising in nanotechnology. Such problems are presented as nonlinear differential–difference equations. The proposed method is based on the Laplace transform with the homotopy analysis method (HAM). This method is a powerful tool for solving a large amount of problems. This technique provides a series of functions which may converge to the exact solution of the problem. A good agreement between the obtained solution and some well-known results is obtained.

Keywords: discretized mKdV lattice equation nonlinear differential–difference equations Laplace transform homotopy analysis transform method

Received: 14 January 2013
Revised: 27 June 2013
Accepted manuscript online:

PACS:	02.20.Sv	(Lie algebras of Lie groups)
	47.15.-x	(Laminar flows)
	44.40.+a	(Thermal radiation)
	44.10.+i	(Heat conduction)

Corresponding Authors: M. M. Khader
E-mail: mohamedmbd@yahoo.com

Cite this article:

M. M. Khader, Sunil Kumar, S. Abbasbandy New homotopy analysis transform method for solving the discontinued problems arising in nanotechnology 2013 Chin. Phys. B 22 110201

[1]	Liao S J 1992 The Proposed Homotopy Analysis Technique for the Solution of Nonlinear Problems (PhD Thesis) (Shanghai: Shanghai Jiao Tong University)
[2]	Liao S J 2003 Beyond Perturbation: Introduction to the Homotopy Analysis Method (Boca Raton: Champan and Hall/CRC Press)
[3]	Liao S J 2004 Appl. Math. Comput. 147 499
[4]	Sweilam N H and Khader M M 2011 World Applied Sciences Journal 13 1
[5]	Vishal K, Kumar S and Das S 2012 Appl. Math. Modell. 36 3630
[6]	Adomian G 1994 Solving Frontier Problems of Physics: The Decomposition Method (Boston: Kluwer Academic Publishers) p. 150
[7]	El-Sayed S M and Kaya D 2004 Appl. Math. Comput. 158 101
[8]	Khader M M and Al-Bar R F 2011 Mathematics Problem Engineering 2011 1
[9]	Sweilam N H and Khader M M 2010 Appl. Math. Comput. 217 495
[10]	Mokhtari R 2008 Int. J. Nonlinear Sci. 9 19
[11]	Sweilam N H and Khader M M 2010 Int. J. Computer Math. 87 1120
[12]	Abbasbandy S 2007 Int. Comm. Heat Mass Transfer 34 380
[13]	Abbasbandy S 2007 Phys. Lett. A 361 478
[14]	Hayat T, Khan M and Asghar S 2004 Acta Mech. 168 213
[15]	Jafari H and Seifi S 2009 Commun. Nonlinear Sci. Numer. Simul. 14 2006
[16]	Jun C, Song-Ping Z and Shi-Jun L 2010 Communications in Nonlinear Science and Numerical Simulation 15 148
[17]	Shun-dong Z, Yu-ming C and Song-liang Q 2009 Computers and Mathematics with Applications 58 2398
[18]	El Naschie M S 2006 Chaos Soliton. Fract. 30 769
[19]	El Naschie M S 2007 Int. J. Nonlinear Sci. 8 5
[20]	El Naschie M S 2007 Int. J. Nonlinear Sci. 8 11
[21]	He J H, Liu Y Y and Xu L 2007 Chaos Soliton. Fract. 32 1096
[22]	He J H and Zhu S D 2008 J. Phys. Conf. Ser. 96 012189
[23]	Suris Y B 1998 Miura transformation for Toda-type Integrable System with Applications to the Problem of Integrable Discretizations (Berlin: Fachbereich Mathematik, Technische University Press)
[24]	Zhu S D 2007 Int. J. Nonlinear Sci. 8 465
[25]	Khan M, Gondal M A, Hussain I and Vanani S 2012 Math. Comput. Modell. 55 1143
[26]	Kumar S, Yildirim A and Leilei W 2012 Scietia Irantica 1117

[1]	Compact finite difference schemes for the backward fractional Feynman-Kac equation with fractional substantial derivative Jiahui Hu(胡嘉卉), Jungang Wang(王俊刚), Yufeng Nie(聂玉峰), Yanwei Luo(罗艳伟). Chin. Phys. B, 2019, 28(10): 100201.
[2]	The bound state solution for the Morse potential with a localized mass profile S Miraboutalebi. Chin. Phys. B, 2016, 25(10): 100301.
[3]	Relativistic effect of pseudospin symmetry and tensor coupling on the Mie-type potential via Laplace transformation method M. Eshghi, S. M. Ikhdair. Chin. Phys. B, 2014, 23(12): 120304.
[4]	Variational iteration method for solving the time-fractional diffusion equations in porous medium Wu Guo-Cheng (吴国成). Chin. Phys. B, 2012, 21(12): 120504.
[5]	Dynamic analysis of a new chaotic system with fractional order and its generalized projective synchronization Niu Yu-Jun(牛玉军), Wang Xing-Yuan(王兴元), Nian Fu-Zhong(年福忠), and Wang Ming-Jun(王明军). Chin. Phys. B, 2010, 19(12): 120507.
[6]	Hyperbolic function method for solving nonlinear differential-different equations Zhu Jia-Min (朱加民). Chin. Phys. B, 2005, 14(7): 1290-1295.
[7]	Exact solutions of N-dimensional harmonic oscillator via Laplace transformation Chen Gang (陈刚). Chin. Phys. B, 2005, 14(6): 1075-1076.

No Suggested Reading articles found!

Viewed

Full text

Abstract

Cited

Metrics
Related Articles

New homotopy analysis transform method for solving the discontinued problems arising in nanotechnology

Cite this article:

Online attention