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New numerical study of Adomian method applied to a diffusion model

N. Ngarhasta (Université de Ouagadougou (FAST), Burkina‐Faso, France)
B. Some (Université de Ouagadougou (FAST), Burkina‐Faso, France)
K. Abbaoui (Université Fergat ABBAS, Sétif (19000), Algérie)
Y. Cherruault (Université Paris VI, Laboratoire MEDIMAT, Paris, France)

Kybernetes

ISSN: 0368-492X

Article publication date: 1 February 2002

Abstract

We prove in this paper the convergence of Adomian method applied to linear or non‐linear diffusion equations. The results show that the convergence of this method is not influenced by the choice of the linear inversible operator L in the equation to be solved. Furthermore we give some particular examples about a new canonical form where the initial value u0 of Adomian series is chosen in some special form which verifies the initial and boundary conditions. Then Adomian series converges to exact solution or all approximated (truncated series) solutions verify these conditions.

Keywords

Citation

Ngarhasta, N., Some, B., Abbaoui, K. and Cherruault, Y. (2002), "New numerical study of Adomian method applied to a diffusion model", Kybernetes, Vol. 31 No. 1, pp. 61-75. https://doi.org/10.1108/03684920210413764

Publisher

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MCB UP Ltd

Copyright © 2002, MCB UP Limited