Computational study of three numerical methods for some linear and nonlinear advection-diffusion-reaction problems
by A.R. Appadu; Jean M-S. Lubuma; N. Mphephu
Progress in Computational Fluid Dynamics, An International Journal (PCFD), Vol. 17, No. 2, 2017

Abstract: In this paper, we use three existing schemes namely, upwind forward Euler, non-standard finite difference (NSFD) and unconditionally positive finite difference (UPFD) schemes to solve two numerical experiments described by a linear and a nonlinear advection-diffusion-reaction equation with constant coefficients. These equations model exponential travelling waves and biofilm growth on a medical implant respectively. We study the exact and numerical dissipative and dispersive properties of the three schemes for both problems. Moreover, L₁ error, dispersion and dissipation errors, at some values of temporal and spatial step sizes have been computed for the three schemes for both problems.

Online publication date: Tue, 28-Feb-2017

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