| Decomposition method for solving parabolic equations in finite domains |
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| 作者姓名： | INC Mustafa |
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| 作者单位： | Department of |
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| 摘 要： | INTRODUCTION The decomposition method was introduced by Adomian(1989;1994)in the1980’s for solving linear and nonlinear functional equations(algebraic,dif-ferential,partial differential equations(PDEs)and systems,integral,differential-delay,integro-differen-tial equations,etc.)(Adomian,1989;1994;Guellal and Cherruault,1995;Adomian et al.,1996;Laffez and Abbaoui,1996;Ndour et al.,1996;Guellal et al.,1997;Abbaoui and Cherruault,1999;Adjedj,1999).This method leads to computable,accurat…
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| 关 键 词： | 抛物线方程 有限域 分解方法 微分方程 边界条件 |
| 收稿时间： | 2005-02-30 |
| 修稿时间： | 2005-05-25 |
Decomposition method for solving parabolic equations in finite domains |
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| INC Mustafa.Decomposition method for solving parabolic equations in finite domains[J].Journal of Zhejiang University Science,2005,6(10):1058-1064. |
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| Authors: | Inc Mustafa |
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| Institution: | (1) Department of Mathematics, Firat University, 23119 Elazig, Turkey |
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| 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. |
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| Keywords: | Adomian decomposition method (ADM) Adomian polynomials Parabolic differential equations |
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