A new technique of using homotopy analysis method for solving high-order nonlinear differential equations

被引：19
作者：
Hassan, Hany N. [1 ]
El-Tawil, Andmagdy A. [2 ]
机构：
[1] Benha Univ, Dept Basic Sci, High Inst Technol, Banha 13512, Egypt
[2] Cairo Univ, Dept Engn Math & Phys, Fac Engn, Giza, Egypt
来源：
MATHEMATICAL METHODS IN THE APPLIED SCIENCES | 2011年 / 34卷 / 06期
关键词：
nonlinear initial value problems; homotopy analysis method; modified HAM; system of differential equations; PERTURBATION METHOD; HEAT-TRANSFER; FLUID; FLOW;
D O I：
10.1002/mma.1400
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, a new technique of homotopy analysis method (HAM) is proposed for solving high-order nonlinear initial value problems. This method improves the convergence of the series solution, eliminates the unneeded terms and reduces time consuming in the standard homotopy analysis method (HAM) by transform the nth-order nonlinear differential equation to a system of n first-order equations. Second-and third-order problems are solved as illustration examples of the proposed method. Copyright (C) 2010 John Wiley & Sons, Ltd.
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收藏
页码：728 / 742
页数：15
相关论文
共 21 条
  • [1] The application of homotopy analysis method to nonlinear equations arising in heat transfer
    Abbasbandy, S.
    [J]. PHYSICS LETTERS A, 2006, 360 (01) : 109 - 113
  • [2] Homotopy analysis method for multiple solutions of the fractional Sturm-Liouville problems
    Abbasbandy, Saeid
    Shirzadi, A.
    [J]. NUMERICAL ALGORITHMS, 2010, 54 (04) : 521 - 532
  • [3] Analytic Solution of the Sharma-Tasso-Olver Equation by Homotopy Analysis Method
    Abbasbandy, Saeid
    Ashtiani, Mahnaz
    Babolian, Esmail
    [J]. ZEITSCHRIFT FUR NATURFORSCHUNG SECTION A-A JOURNAL OF PHYSICAL SCIENCES, 2010, 65 (04): : 285 - 290
  • [4] Explicit series solutions of some linear and nonlinear Schrodinger equations via the homotopy analysis method
    Alomari, A. K.
    Noorani, M. S. M.
    Nazar, R.
    [J]. COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2009, 14 (04) : 1196 - 1207
  • [5] [Anonymous], THESIS SHANGHAI J TO
  • [6] [Anonymous], 2004, APPL MECH REV
  • [7] Exact flow of a third grade fluid past a porous plate using homotopy analysis method
    Ayub, M
    Rasheed, A
    Hayat, T
    [J]. INTERNATIONAL JOURNAL OF ENGINEERING SCIENCE, 2003, 41 (18) : 2091 - 2103
  • [8] Modified homotopy analysis method for solving systems of second-order BVPs
    Bataineh, A. Sami
    Noorani, M. S. M.
    Hashim, I.
    [J]. COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2009, 14 (02) : 430 - 442
  • [9] On a new reliable modification of homotopy analysis method
    Bataineh, A. Sami
    Noorani, M. S. M.
    Hashim, I.
    [J]. COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2009, 14 (02) : 409 - 423
  • [10] Solving systems of ODEs by homotopy analysis method
    Bataineh, A. Sami
    Noorani, M. S. M.
    Hashim, I.
    [J]. COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2008, 13 (10) : 2060 - 2070
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