Full Text:   <1579>

CLC number: TP391

On-line Access: 

Received: 

Revision Accepted: 2005-05-25

Crosschecked: 0000-00-00

Cited: 3

Clicked: 4519

Citations:  Bibtex RefMan EndNote GB/T7714

-   Go to

Article info.
1. Reference List
Open peer comments

Journal of Zhejiang University SCIENCE A 2005 Vol.6 No.10 P.1058~1064

10.1631/jzus.2005.A1058


Decomposition method for solving parabolic equations in finite domains


Author(s):  INC Mustafa

Affiliation(s):  Department of Mathematics, Firat University, Elazig 23119, Turkey

Corresponding email(s):   minc@firat.edu.tr

Key Words:  Adomian decomposition method (ADM), Adomian polynomials, Parabolic differential equations


INC Mustafa. Decomposition method for solving parabolic equations in finite domains[J]. Journal of Zhejiang University Science A, 2005, 6(10): 1058~1064.

@article{title="Decomposition method for solving parabolic equations in finite domains",
author="INC Mustafa",
journal="Journal of Zhejiang University Science A",
volume="6",
number="10",
pages="1058~1064",
year="2005",
publisher="Zhejiang University Press & Springer",
doi="10.1631/jzus.2005.A1058"
}

%0 Journal Article
%T Decomposition method for solving parabolic equations in finite domains
%A INC Mustafa
%J Journal of Zhejiang University SCIENCE A
%V 6
%N 10
%P 1058~1064
%@ 1673-565X
%D 2005
%I Zhejiang University Press & Springer
%DOI 10.1631/jzus.2005.A1058

TY - JOUR
T1 - Decomposition method for solving parabolic equations in finite domains
A1 - INC Mustafa
J0 - Journal of Zhejiang University Science A
VL - 6
IS - 10
SP - 1058
EP - 1064
%@ 1673-565X
Y1 - 2005
PB - Zhejiang University Press & Springer
ER -
DOI - 10.1631/jzus.2005.A1058


Abstract: 
This paper presents a comparison among adomian decomposition method (ADM), Wavelet-Galerkin method (WGM), the fully explicit (1,7) finite difference technique (FTCS), the fully implicit (7,1) finite difference method (BTCS), (7,7) Crank-Nicholson type finite difference formula (C-N), the fully explicit method (1,13) and 9-point finite difference method, for solving parabolic differential equations with arbitrary boundary conditions and based on weak form functionals in finite domains. The problem is solved rapidly, easily and elegantly by ADM. The numerical results on a 2D transient heat conducting problem and 3D diffusion problem are used to validate the proposed ADM as an effective numerical method for solving finite domain parabolic equations. The numerical results showed that our present method is less time consuming and is easier to use than other methods. In addition, we prove the convergence of this method when it is applied to the nonlinear parabolic equation.

Darkslateblue:Affiliate; Royal Blue:Author; Turquoise:Article

Reference

[1] Abbaoui, K., Cherruault, Y., 1999. The decomposition method applied to the Cauchy problem. Kybernetes, 28(1):68-74.

[2] Abbaoui, K., Pujol, M.J., Cherruault, Y., Himoun, N., Grimalt, P., 2001. A new formulation of Adomian method, convergence results. Kybernetes, 30(9/10):1183-1191.

[3] Adjedj, B., 1999. Application of the decomposition method to the understanding of HIV immune dynamics. Kybernetes, 28(3):271-283.

[4] Adomian, G., 1989. Nonlinear Stochastic Systems and Applications to Physics. Kluwer Academic Press, Boston.

[5] Adomian, G., 1994. Solving Frontier Problems of Physics: The Decomposition Method. Kluwer Academic Press, Boston.

[6] Adomian, G., Cherruault, Y., Abbaoui, K., 1996. A nonperturbative analytical solution of immune response with time-delays and possible generalization. Math. Comput. Modelling, 20(10):89-96.

[7] Cannon, J.R., Hoek, J., 1986. Diffusion subject to specification of mass. J. Math. Anal. Applic., 115:517-529.

[8] Cannon, J.R., Matheson, A.L., 1993. A numerical procedure of diffusion subject to the specification of mass. Int. J. Eng. Sci., 31:347-354.

[9] Cannon, J.R., Lin, Y., Wang, S., 1990. An implicit finite difference scheme for diffusion equation subject to mass specification. Int. J. Eng. Sci., 28(7):573-578.

[10] Capso, V., Kunisch, K., 1988. A reaction-diffusion system arising in modeling man-environment diseases. Quart. Appl. Math., 46:431-449.

[11] Cherruault, Y., 1989. Convergence of Adomian’s method. Kybernetes, 18(1):31-38.

[12] Cherruault, Y., Adomian, G., 1993. Decomposition method: A new proof of convergence. Math. Comput. Modelling, 18:103-106.

[13] Dehghan, M., 2002. Fully explicit finite-difference methods for two-dimensional diffusion with an integral condition. Nonlinear Analysis, 48:637-650.

[14] Dehghan, M., 2003a. Parallel techniques for a boundary value problem with non-classic boundary conditions. Appl. Math. Comput., 137:399-412.

[15] Dehghan, M., 2003b. Numerical solution of a parabolic equation with non-local boundary specification. Appl. Math. Comput., 145:185-194.

[16] El-Sayed, S.M., Abdel-Aziz, M.R., 2003. A comparison of Adomian’s decomposition method and Wavelet-Galerkin method for solving integro-differential equations. Appl. Math. Comput., 136:151-159.

[17] Guellal, S., Cherruault, Y., 1995. Application of the decomposition method to identify the disturbed parameters of an elliptical equation. Math. Comput. Modelling, 21(4):51-55.

[18] Guellal, S., Grimalt, P., Cherruault, Y., 1997. Numerical study of Lorentz’s equation by the Adomian method. Comput. Math. Applic., 33(3):25-29.

[19] Ho, S.L., Yang, S.Y., 2001. Wavelet-Galerkin method for solving parabolic equations in finite domains. Finite Elements in Analysis and Design, 37:1023-1037.

[20] Laffez, P., Abbaoui, K., 1996. Modelling of the thermic exchanges during a drilling. Resolution with Adomian’s method. Math. Comput. Modelling, 21(4):51-55.

[21] Lesnic, D., 2002a. Convergence of Adomian’s method: Periodic temperatures. Comput. Math. Applic., 44:13-24.

[22] Lesnic, D., 2002b. The decomposition method for forward and backward time-dependent problems. J. Comput. Appl. Math., 147:27-39.

[23] Ndour, M., Abbaoui, K., Ammar, H., Cherruault, Y., 1996. An example of an interaction model between two species. Kybernetes, 25(4):106-118.

[24] Ngarhasta, N., Some, B., Abbaoui, K., Cherruault, Y., 2002. New numerical study of Adomian method applied to a diffusion model. Kybernetes, 31(1):61-75.

[25] Sanchez, F., Abbaoui, K., Cherruault, Y., 2000. Beyond the thin-sheet approximation: Adomian’s decomposition. Optics Commun., 173:397-401.

[26] Wang, S., 1990. The numerical method for the heat conduction subject to moving boundary energy specification. Numer. Heat. Transfer, 130:35-38.

Open peer comments: Debate/Discuss/Question/Opinion

<1>

Naftali Indongo@Research<naftalindeapo@gmail.com>

2014-08-30 20:42:55

Would love to use it as a reference to my thesis

Ogugua Onyejekwe@No address<oguguao@yahoo.com>

2012-02-24 01:24:40

to review the article



I. N. Njoseh@DELSU<njoseh@delsung.net>

2011-07-05 15:52:04

I will like to receive/see the full article pls.

Dr Ghulam Muhammad@Retired<gm.sheikh@hotmail.com>

2010-11-07 01:02:10

Please let me recieve the full text of this paper
thanks

K.C.MISHRA@NIT HAMIRPUR<kcm80@rediffmail.com>

2010-10-04 14:10:13

to review the article

Please provide your name, email address and a comment





Journal of Zhejiang University-SCIENCE, 38 Zheda Road, Hangzhou 310027, China
Tel: +86-571-87952783; E-mail: cjzhang@zju.edu.cn
Copyright © 2000 - Journal of Zhejiang University-SCIENCE