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.