A new approach to solve a diffusion-convection problem

ISSN： 0368-492X

Source： Kybernetes: The International Journal of Systems & Cybernetics, Vol.31, Iss.3-4, 2002-07, pp. : 536-549

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Abstract

We use the Adomian decomposition method to study a non-linear diffusion-convection problem (NDCP). The decomposition method has been applied recently to a wide class of non-linear stochastic and deterministic operator equations involving algebraic, differential, integro-differential and partial differential equations and systems. The method provides a solution without linearization, perturbation, or unjustified assumptions. An analytic solution of NDCP in the form of a series with easily computable components using the decomposition method will be determined. The non-homogeneous equation is effectively solved by employing the phenomena of the self-cancelling `noise terms' whose sum vanishes in the limit. Comparing the methodology with some known techniques shows that the present approach is highly accurate.