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ZJUS-A
Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering)  2005, Vol. 6 Issue (10): 1058-1064    DOI: 10.1631/jzus.2005.A1058
Computer & Information Science     
Decomposition method for solving parabolic equations in finite domains
INC Mustafa
Department of Mathematics, Firat University, Elazig 23119, 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.

Key words： Adomian decomposition method (ADM)      Adomian polynomials      Parabolic differential equations     
CLC:  TP391  
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INC Mustafa. Decomposition method for solving parabolic equations in finite domains. Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering), 2005, 6(10): 1058-1064.

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http://www.zjujournals.com/xueshu/zjus-a/10.1631/jzus.2005.A1058     OR     http://www.zjujournals.com/xueshu/zjus-a/Y2005/V6/I10/1058

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