Explicit series solutions of some linear and nonlinear Schrodinger equations via the homotopy analysis method

被引：51

作者：

Alomari, A. K. ^{[1
]}

Noorani, M. S. M. ^{[1
]}

Nazar, R. ^{[1
]}

机构：

[1] Univ Kebangsaan Malaysia, Sch Math Sci, Fac Sci & Technol, Bangi 43600, Selangor, Malaysia

来源：

COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION | 2009年 / 14卷 / 04期

关键词：

Schrodinger equation; Homotopy analysis method; Analytical solution; Series solution; APPROXIMATE SOLUTION TECHNIQUE; ANALYTIC SOLUTION; SMALL PARAMETERS; GRADE FLUID; FLOW;

D O I：

10.1016/j.cnsns.2008.01.008

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, by means of the homotopy analysis method (HAM), the solutions of some Schrodinger equations are exactly obtained in the form of convergent Taylor series. The HAM contains the auxiliary parameter h, that provides a convenient way of controlling the convergent region of series solutions. This analytical method is employed to solve linear and nonlinear examples to obtain the exact solutions. HAM is a powerful and easy-to-use analytic tool for nonlinear problems. (C) 2008 Elsevier B.V. All rights reserved.

引用

页码：1196 / 1207

页数：12

共 32 条

[1] The application of homotopy analysis method to nonlinear equations arising in heat transfer [J].

Abbasbandy, S. .

PHYSICS LETTERS A, 2006, 360 (01) :109-113

[2]

ABBASBANDY S, 2006, PHYS LETT A, V15, P1

[3] NOISE TERMS IN DECOMPOSITION SOLUTION SERIES [J].

ADOMIAN, G ;

RACH, R .

COMPUTERS & MATHEMATICS WITH APPLICATIONS, 1992, 24 (11) :61-64

[4]

Adomian G., 1994, Solving Frontier Problems of Physics: the Decomposition Method

[5] Exact flow of a third grade fluid past a porous plate using homotopy analysis method [J].

Ayub, M ;

Rasheed, A ;

Hayat, T .

INTERNATIONAL JOURNAL OF ENGINEERING SCIENCE, 2003, 41 (18) :2091-2103

[6] Solving systems of ODEs by homotopy analysis method [J].

Bataineh, A. Sami ;

Noorani, M. S. M. ;

Hashim, I. .

COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2008, 13 (10) :2060-2070

[7] Application of variational iteration method to heat-and wave-like equations [J].

Batiha, B. ;

Noorani, M. S. M. ;

Hashim, I. .

PHYSICS LETTERS A, 2007, 369 (1-2) :55-61

[8] Approximate analytical solution for the Zakharov-Kuznetsov equations with fully nonlinear dispersion [J].

Batiha, Khaldoun .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2008, 216 (01) :157-163

[9] 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

[10] Solving Riccati differential equation using Adomian's decomposition method [J].

El-Tawil, MA ;

Bahnasawi, AA ;

Abdel-Naby, A .

APPLIED MATHEMATICS AND COMPUTATION, 2004, 157 (02) :503-514

← 1 2 3 4 →