A Modified Laplace-Homotopy Perturbation Algorithm

PENG Bo; TANG Shuo

doi:10.3879/j.issn.1000-0887.2015.07.009

Volume 36 Issue 7

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PENG Bo, TANG Shuo. A Modified Laplace-Homotopy Perturbation Algorithm[J]. Applied Mathematics and Mechanics, 2015, 36(7): 768-778. doi: 10.3879/j.issn.1000-0887.2015.07.009

Citation:

PENG Bo, TANG Shuo. A Modified Laplace-Homotopy Perturbation Algorithm[J]. Applied Mathematics and Mechanics, 2015, 36(7): 768-778. doi: 10.3879/j.issn.1000-0887.2015.07.009

Citation:

PENG Bo, TANG Shuo. A Modified Laplace-Homotopy Perturbation Algorithm[J]. Applied Mathematics and Mechanics, 2015, 36(7): 768-778. doi: 10.3879/j.issn.1000-0887.2015.07.009

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A Modified Laplace-Homotopy Perturbation Algorithm

doi: 10.3879/j.issn.1000-0887.2015.07.009

PENG Bo,
TANG Shuo

School of Mathematics, Hefei University of Technology, Hefei 230009, P.R.China

Funds: The National Natural Science Foundation of China(61272024)

Received Date: 2014-12-24
Rev Recd Date: 2015-03-09
Publish Date: 2015-07-15

Abstract

Abstract

A modified NDLT-HPM (MNDLT-HPM for short) was proposed through introduction of a parameter into the NDLT-HPM (nonlinearities distribution Laplace transform-homotopy perturbation method). This parameter makes the solving process for the nonlinear differential equations more flexible and is able to adjust and control the convergence region of the series solution, meanwhile overcomes the limitations of the NDLT-HPM that the series solution may be non-convergent when embedded parameter p equals 1. The present algorithm gives series solutions which converge well to the corresponding exact ones, thus obtaining sufficiently accurate approximate analytical solutions. 2 numerical examples show the advantage and accuracy of this method.
- NDLT-HPM,
- MNDLT-HPM,
- parameter,
- differential equation

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References(20)

References

[1]	搂森岳, 唐晓艳. 非线性数学物理方法[M]. 北京: 科学出版社, 2006.(LOU Sen-yue, TANG Xiao-yan. The Method of Nonlinear Mathematical and Physical[M]. Beijing: Science Press, 2006.(in Chinese))
[2]	谷超豪, 胡和生, 周子翔. 孤立子理论中的达布变换及其几何应用[M]. 上海: 上海科学技术出版社, 1999.(GU Chao-hao, HU He-sheng, ZHOU Zi-xiang. Darboux Transformation in Soliton Theory and Its Geometric Applications[M]. Shanghai: Shanghai Scientific & Technical Publishers, 1999.(in Chinese))
[3]	陈登远. 孤子引论[M]. 北京: 科学出版社, 2006.(CHEN Deng-yuan. Soliton Introduction[M]. Beijing: Science Press, 2006.(in Chinese))
[4]	Ablowit M J, Clarkson P A. Solitons Nonlinear Evolution Equations and Inverse Scattering[M]. 世界图书出版公司北京公司, 2000.
[5]	Golbabai A, Javidi M. A third-order Newton type method for nonlinear equations based on modified homotopy perturbation method[J]. Applied Mathematics and Computation,2007,191(1): 199-205.
[6]	WANG Fei, LI Wei, ZHANG Hong-qing. A new extended homotopy perturbation method for nonlinear differential equations[J]. Mathematical and Computer Modelling,2012,55(3/4): 1471-1477.
[7]	HE Ji-huan. Homotopy perturbation method: a new nonlinear analytical technique[J]. Applied Mathematics and Computation,2003,135(1): 73-79.
[8]	Biazar J, Ghazvini H. Convergence of the homotopy perturbation method for partial differential equations[J]. Nonlinear Analysis: Real World Applications,2009,10(6): 2633-2640.
[9]	Adomian G. Nonlinear stochastic differential equations[J]. Journal of Mathematical Analysis and Applications,1976,12(55): 441- 452.
[10]	Adomian G, Adomian G E. A global method for solution of complex systems[J]. Mathematical Modelling,1984, 5(4): 251-263.
[11]	Lyapunov A M. The General Problem on Stability of Motion[M]. London: Taylor & Francis, 1992.
[12]	Skirmishing A V, Zhukov A T, Kolovos V G. Methods of Dynamics Calculation and Testing for Thin-Walled Structures[M]. Moscow: Mashinoxstroyenie, 1990.
[13]	LIAO Shi-jun. Proposed homotopy analysis technique for the solution of nonlinear problems[D]. Ph D Thesis. Shanghai: Shanghai Jiao Tong University, 1992.
[14]	LIAO Shi-jun. A kind of approximate solution technique which does not depend upon small parameters—II: an application in fluid mechanics[J]. International Journal of Non-Linear Mechanics,1997,32(5): 815-822.
[15]	Filobello-Nino U, Vazquez-Leal H, Benhammouda B, Hernandez-Martinez L, Hoyos-Reyes C, Perez-Sesma J A, Jimenez-Fernandez V M, Pereyra-Diaz D, Marin-Hernandez A, Diaz-Sanchez A, Huerta-Chua J, Cervantes-Perez J. Nonlinearities distribution Laplace transform-homotopy perturbation method[J]. Springer Plus,2014,28(3): 1-13.
[16]	Vazquez-Leal H, Sarmiento-Reyes A, Khan Y, Flabella-Nino U, Diaz-Sanchez A. Rational biparameter homotopy perturbation method and Laplace-Paden coupled version[J]. Journal of Applied Mathematics,2012,23(21): 456-467.
[17]	LIAO Shi-jun. Beyond Perturbation: Introduction to the Homotopy Analysis Method[M]. Chapman & Hall/Croppers, 2003.
[18]	Marinca V, Harrison N. Application of optimal homotopy asymptotic method for solving nonlinear equations arising in heat transfer[J]. International Communications in Heat and Mass Transfer,2008,35(6): 710-715.
[19]	Marinca V, Hersanu N. An optimal homotopy asymptotic method applied to the steady flow of a fourth-grade fluid past a porous plate[J]. Applied Mathematics Letters,2009,22(2): 245-251.
[20]	牛照. 非线性问题中的优化同伦分析方法[D]. 硕士学位论文. 上海: 上海交通大学, 2010.(NIU Zhao. Optimized homotopy method in nonlinear problem[D]. Master Thesis. Shanghai: Shanghai Jiao Tong University, 2010.(in Chinese))