An efficient method for quadratic Riccati differential equation

被引：51

作者：

Aminikhah, Hossein ^{[1
]}

Hemmatnezhad, Milad ^{[2
]}

机构：

[1] Shahrood Univ Technol, Sch Math Sci, Dept Math, Shahrood, Iran

[2] Univ Guilan, Dept Mech Engn, Rasht, Iran

来源：

COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION | 2010年 / 15卷 / 04期

关键词：

NHPM; Nonlinear equations; Riccati equation; Taylor series expansion; HOMOTOPY-PERTURBATION METHOD; THIN-FILM FLOW; 3RD-GRADE FLUID; HEAT-TRANSFER;

D O I：

10.1016/j.cnsns.2009.05.009

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, a new form of homotopy perturbation method (NHPM) has been adopted for solving the quadratic Riccati differential equation. In this technique, the solution is considered as a Taylor series expansion converges rapidly to the exact solution of the nonlinear equation. Having found the exact solution of the Riccati equation, the capability and the simplicity of the proposed technique is clarified. (C) 2009 Elsevier B.V. All rights reserved.

引用

页码：835 / 839

页数：5

共 28 条

[1] A new application of He's variational iteration method for quadratic Riccati differential equation by using Adomian's polynomials [J].

Abbasbandy, S. .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2007, 207 (01) :59-63

[2] Iterated He's homotopy perturbation method for quadratic Riccati differential equation [J].

Abbasbandy, S. .

APPLIED MATHEMATICS AND COMPUTATION, 2006, 175 (01) :581-589

[3] A numerical solution of Blasius equation by Adomian's decomposition method and comparison with homotopy perturbation method [J].

Abbasbandy, S. .

CHAOS SOLITONS & FRACTALS, 2007, 31 (01) :257-260

[4] Numerical solutions of the integral equations: Homotopy perturbation method and Adomian's decomposition method [J].

Abbasbandy, S .

APPLIED MATHEMATICS AND COMPUTATION, 2006, 173 (01) :493-500

[5] Homotopy perturbation method for quadratic Riccati differential equation and comparison with Adomian's decomposition method [J].

Abbasbandy, S .

APPLIED MATHEMATICS AND COMPUTATION, 2006, 172 (01) :485-490

[6] Exact solutions for non-linear Schrodinger equations by He's homotopy perturbation method [J].

Biazar, J. ;

Ghazvini, H. .

PHYSICS LETTERS A, 2007, 366 (1-2) :79-84

[7] Homotopy-perturbation method for pure nonlinear differential equation [J].

Cveticanin, L. .

CHAOS SOLITONS & FRACTALS, 2006, 30 (05) :1221-1230

[8] Application of homotopy-perturbation and variational iteration methods to nonlinear heat transfer and porous media equations [J].

Ganji, D. D. ;

Sadighi, A. .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2007, 207 (01) :24-34

[9] The application of He's homotopy perturbation method to nonlinear equations arising in heat transfer [J].

Ganji, D. D. .

PHYSICS LETTERS A, 2006, 355 (4-5) :337-341

[10] Homotopy perturbation method for solving boundary value problems [J].

He, JH .

PHYSICS LETTERS A, 2006, 350 (1-2) :87-88

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