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A new approach to solve a diffusion-convection problem. (English) Zbl 1015.65053

Summary: We use the Adomian decomposition method to study a nonlinear diffusion-convection problem (NDCP). The decomposition method has been applied recently to a wide class of nonlinear 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.

65M70Spectral, collocation and related methods (IVP of PDE)
35K55Nonlinear parabolic equations