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.
引用
收藏
页码：728 / 742
页数：15
相关论文
共 50 条
  • [41] High-Order Schemes for Nonlinear Fractional Differential Equations
    Alsayyed, Omar
    Awawdeh, Fadi
    Al-Shara', Safwan
    Rawashdeh, Edris
    FRACTAL AND FRACTIONAL, 2022, 6 (12)
  • [42] Solving a System of Linear and Nonlinear Fractional Partial Differential Equations Using Homotopy Perturbation Method
    Matinfar, M.
    Saeidy, M.
    Eslami, M.
    INTERNATIONAL JOURNAL OF NONLINEAR SCIENCES AND NUMERICAL SIMULATION, 2013, 14 (7-8) : 471 - 478
  • [43] An efficient spectral method for high-order nonlinear integro-differential equations
    Sohrabi, Saeed
    UPB Scientific Bulletin, Series A: Applied Mathematics and Physics, 2012, 74 (03): : 75 - 88
  • [44] On the Bivariate Spectral Homotopy Analysis Method Approach for Solving Nonlinear Evolution Partial Differential Equations
    Motsa, S. S.
    ABSTRACT AND APPLIED ANALYSIS, 2014,
  • [45] AN EFFICIENT SPECTRAL METHOD FOR HIGH-ORDER NONLINEAR INTEGRO-DIFFERENTIAL EQUATIONS
    Sohrabi, Saeed
    UNIVERSITY POLITEHNICA OF BUCHAREST SCIENTIFIC BULLETIN-SERIES A-APPLIED MATHEMATICS AND PHYSICS, 2012, 74 (03): : 75 - 88
  • [46] High-order quantum algorithm for solving linear differential equations
    Berry, Dominic W.
    JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 2014, 47 (10)
  • [47] Solving High-Order Uncertain Differential Equations via Runge-Kutta Method
    Ji, Xiaoyu
    Zhou, Jian
    IEEE TRANSACTIONS ON FUZZY SYSTEMS, 2018, 26 (03) : 1379 - 1386
  • [48] MIM: A deep mixed residual method for solving high-order partial differential equations
    Lyu, Liyao
    Zhang, Zhen
    Chen, Minxin
    Chen, Jingrun
    JOURNAL OF COMPUTATIONAL PHYSICS, 2022, 452
  • [49] Solving high-order uncertain differential equations via Adams-Simpson method
    Hou, Yudong
    Wu, Lijun
    Sheng, Yuhong
    COMPUTATIONAL & APPLIED MATHEMATICS, 2021, 40 (07):
  • [50] Homotopy perturbation method for nonlinear partial differential equations of fractional order
    Momani, Shaher
    Odibat, Zaid
    PHYSICS LETTERS A, 2007, 365 (5-6) : 345 - 350
12345