A Convergence Analysis of a Multistep Method Applied to an Advection-Diffusion Equation in 1-D.

This paper describes a method for convection-dominated fluid or heat flows. This method relies on the Hopmoc method and backward differentiation formulas. The present study discusses the convergence of the method when applied to a convection-diffusion equation in 1-D. The convergence analysis conducted produced sufficient conditions for the consistency analysis and used the von Neumann analysis to demonstrate that the method is stable. Moreover, the numerical results confirmed the conducted convergence analysis.