A new approach to solve a diffusion‐convection problem

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.