Solution of coupled system of nonlinear differential equations using homotopy analysis method

被引：15

作者：

Ganjiani, Mehdi ^{[1
]}

Ganjiani, Hossein ^{[2
]}

机构：

[1] Sharif Univ Technol, Dept Mech Engn, Tehran, Iran

[2] Shaheed Beheshti Univ, Dept Nucl Engn, Tehran 1983963113, Iran

来源：

NONLINEAR DYNAMICS | 2009年 / 56卷 / 1-2期

关键词：

Homotopy analysis method; Numerical solution; Coupled system of nonlinear equations; APPROXIMATE SOLUTION TECHNIQUE; VARIATIONAL ITERATION METHOD; TRAVELING-WAVE SOLUTIONS; DE VRIES EQUATION; KDV EQUATION; NONCOMPACT STRUCTURES; EVOLUTION-EQUATIONS; SMALL PARAMETERS; VARIANTS; COMPACT;

D O I：

10.1007/s11071-008-9386-7

中图分类号：

TH [机械、仪表工业];

学科分类号：

0802 ;

摘要：

In this article, the homotopy analysis method has been applied to solve a coupled nonlinear diffusion-reaction equations. The validity of this method has been successful by applying it for these nonlinear equations. The results obtained by this method have a good agreement with one obtained by other methods. This work illustrates the validity of the homotopy analysis method for the nonlinear differential equations. The basic ideas of this approach can be widely employed to solve other strongly nonlinear problems.

引用

页码：159 / 167

页数：9

共 50 条

[1] Solution of coupled system of nonlinear differential equations using homotopy analysis method
Mehdi Ganjiani
Hossein Ganjiani
Nonlinear Dynamics, 2009, 56 : 159 - 167
[2] Solution of nonlinear fractional differential equations using homotopy analysis method
Ganjiani, Mehdi
APPLIED MATHEMATICAL MODELLING, 2010, 34 (06) : 1634 - 1641
[3] The solution of a coupled system of nonlinear physical problems using the homotopy analysis method
El-Wakil, S. A.
Abdou, M. A.
PHYSICA SCRIPTA, 2010, 81 (01)
[4] 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
[5] Analysis of Fractional Nonlinear Differential Equations Using the Homotopy Perturbation Method
Balci, Mehmet Ali
Yildirim, Ahmet
ZEITSCHRIFT FUR NATURFORSCHUNG SECTION A-A JOURNAL OF PHYSICAL SCIENCES, 2011, 66 (1-2): : 87 - 92
[6] Solution of fuzzy fractional differential equations using homotopy analysis method
Lee, Meng Oon
Kumaresan, N.
Ratnavelu, Kuru
MATEMATIKA, 2016, 32 (02) : 113 - 119
[7] Numerical Solution of Nonlinear Fredholm Integro-Differential Equations Using Spectral Homotopy Analysis Method
Atabakan, Z. Pashazadeh
Nasab, A. Kazemi
Kilicman, A.
Eshkuvatov, Zainidin K.
MATHEMATICAL PROBLEMS IN ENGINEERING, 2013, 2013
[8] Homotopy perturbation transform method with he's polynomial for solution of coupled nonlinear partial differential equations
Sharma D.
Singh P.
Chauhan S.
Nonlinear Engineering, 2016, 5 (01) : 17 - 23
[9] 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
[10] The Solution of the Linear Fractional Partial Differential Equations Using the Homotopy Analysis Method
Dehghan, Mehdi
Manafian, Jalil
Saadatmandi, Abbas
ZEITSCHRIFT FUR NATURFORSCHUNG SECTION A-A JOURNAL OF PHYSICAL SCIENCES, 2010, 65 (11): : 935 - 949

← 1 2 3 4 5 →