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
  • [1] A new technique of using homotopy analysis method for second order nonlinear differential equations
    Hassan, Hany N.
    El-Tawil, Magdy A.
    APPLIED MATHEMATICS AND COMPUTATION, 2012, 219 (02) : 708 - 728
  • [2] Solving Nonlinear Fractional Partial Differential Equations Using the Homotopy Analysis Method
    Dehghan, Mehdi
    Manafian, Jalil
    Saadatmandi, Abbas
    NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, 2010, 26 (02) : 448 - 479
  • [3] A HIGH-ORDER PREDICTOR-CORRECTOR METHOD FOR SOLVING NONLINEAR DIFFERENTIAL EQUATIONS OF FRACTIONAL ORDER
    Thien Binh Nguyen
    Jang, Bongsoo
    FRACTIONAL CALCULUS AND APPLIED ANALYSIS, 2017, 20 (02) : 447 - 476
  • [4] A High-Order Predictor-Corrector Method for Solving Nonlinear Differential Equations of Fractional Order
    Thien Binh Nguyen
    Bongsoo Jang
    Fractional Calculus and Applied Analysis, 2017, 20 : 447 - 476
  • [5] Solving high-order nonlinear differential equations using operational matrix based on exponential collocation method
    Aslefallah, Mohammad
    Abbasbandy, Saeid
    Yuzbasi, Suayip
    SIGMA JOURNAL OF ENGINEERING AND NATURAL SCIENCES-SIGMA MUHENDISLIK VE FEN BILIMLERI DERGISI, 2023, 41 (04): : 689 - 698
  • [6] Solving a system of nonlinear fractional partial differential equations using homotopy analysis method
    Jafari, H.
    Seifi, S.
    COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2009, 14 (05) : 1962 - 1969
  • [7] Analysis of Homotopy Perturbation Method for Solving Fractional Order Differential Equations
    Javeed, Shumaila
    Baleanu, Dumitru
    Waheed, Asif
    Khan, Mansoor Shaukat
    Affan, Hira
    MATHEMATICS, 2019, 7 (01)
  • [8] Solving Nonlinear, High-Order Partial Differential Equations Using a High-Performance Isogeometric Analysis Framework
    Cortes, Adriano M. A.
    Vignal, Philippe
    Sarmiento, Adel
    Garcia, Daniel
    Collier, Nathan
    Dalcin, Lisandro
    Calo, Victor M.
    HIGH PERFORMANCE COMPUTING, CARLA 2014, 2014, 485 : 236 - 247
  • [9] Generalized homotopy method for solving nonlinear differential equations
    Hector Vazquez-Leal
    Computational and Applied Mathematics, 2014, 33 : 275 - 288
  • [10] Generalized homotopy method for solving nonlinear differential equations
    Vazquez-Leal, Hector
    COMPUTATIONAL & APPLIED MATHEMATICS, 2014, 33 (01): : 275 - 288
12345