HYBRID ANALYSIS OF TRANSIENT NON‐LINEAR CONVECTION‐DIFFUSION PROBLEMS

Abstract

A hybrid numerical‐analytical approach, based on recent developments in the generalized integral transform technique, is presented for the solution of a class of non‐linear transient convection‐diffusion problems. The original partial differential equation is integral transformed into a denumerable system of coupled non‐linear ordinary differential equations, which is numerically solved for the transformed potentials. The hybrid analysis convergence is illustrated by considering the one‐dimensional non‐linear Burgers equation and numerical results are presented for increasing truncation orders of the infinite ODE system.