Adomian's decomposition method and homotopy perturbation method in solving nonlinear equations

被引：25

作者：

Li, Jian-Lin ^{[1
]}

机构：

[1] Shaanxi Normal Univ, Coll Math & Informat Sci, Xian 710062, Peoples R China

来源：

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2009年 / 228卷 / 01期

基金：

中国国家自然科学基金;

关键词：

Adomian's decomposition method (ADM); Homotopy perturbation method (HPM); Nonlinear equations; ITERATIVE METHODS; CONVERGENCE; POLYNOMIALS;

D O I：

10.1016/j.cam.2008.09.007

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The Adomian's decomposition method and the homotopy perturbation method are two powerful methods which consider the approximate solution of a nonlinear equation as an infinite series usually converging to the accurate solution. By theoretical analysis of the two methods, we show, in the present paper, that the two methods are equivalent in solving nonlinear equations. (c) 2008 Elsevier B.V. All rights reserved.

引用

页码：168 / 173

页数：6

共 50 条

[1] The Homotopy Perturbation Method and the Adomian Decomposition Method for the Nonlinear Coupled Equations
Zayed, E. M. E.
Rahman, Abdel H. M.
[J]. JOURNAL OF PARTIAL DIFFERENTIAL EQUATIONS, 2009, 22 (04): : 334 - 351
[2] Modified homotopy perturbation method for nonlinear equations and comparison with Adomian decomposition method
Abbasbandy, S
[J]. APPLIED MATHEMATICS AND COMPUTATION, 2006, 172 (01) : 431 - 438
[3] Numerical solutions of the integral equations: Homotopy perturbation method and Adomian's decomposition method
Abbasbandy, S
[J]. APPLIED MATHEMATICS AND COMPUTATION, 2006, 173 (01) : 493 - 500
[4] Comparing Homotopy Perturbation Method and Adomian Decomposition Method
Biazar, Jafar
Ayati, Zainab
Ebrahimi, Hamideh
[J]. NUMERICAL ANALYSIS AND APPLIED MATHEMATICS, 2008, 1048 : 80 - 86
[5] Homotopy analysis method for solving a couple of evolution equations and comparison with Adomian's decomposition method
Jafari, H.
Tajadodi, H.
Biswas, Anjan
[J]. WAVES IN RANDOM AND COMPLEX MEDIA, 2011, 21 (04) : 657 - 667
[6] Adomian's Decomposition Method and Homotopy Perturbation Method in Solving Two-Dimensional Volterra-Fredholm Fuzzy Integral Equations
Georgieva, Atanaska
Naydenova, Iva
[J]. SEVENTH INTERNATIONAL CONFERENCE ON NEW TRENDS IN THE APPLICATIONS OF DIFFERENTIAL EQUATIONS IN SCIENCES (NTADES 2020), 2021, 2321
[7] Equivalence between Homotopy Perturbation Method and Adomian Decomposition Method in Solving Two Dimensional Linear Fredholm Integral Equations
Almousa, Mohammad
Ismail, Ahmad Izani Md
[J]. INTERNATIONAL CONFERENCE ON QUANTITATIVE SCIENCES AND ITS APPLICATIONS (ICOQSIA 2014), 2014, 1635 : 45 - 51
[8] An Improvement to the Homotopy Perturbation Method for Solving Nonlinear Duffing's Equations
Vahidi, A. R.
Babolian, E.
Azimzadeh, Z.
[J]. BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY, 2018, 41 (02) : 1105 - 1117
[9] An Improvement to the Homotopy Perturbation Method for Solving Nonlinear Duffing’s Equations
A. R. Vahidi
E. Babolian
Z. Azimzadeh
[J]. Bulletin of the Malaysian Mathematical Sciences Society, 2018, 41 : 1105 - 1117
[10] Revised Adomian decomposition method for solving a system of nonlinear equations
Jafari, Hossein
Daftardar-Gejji, Varsha
[J]. APPLIED MATHEMATICS AND COMPUTATION, 2006, 175 (01) : 1 - 7

← 1 2 3 4 5 →