Appadu, A. RaoLubuma, Jean M.-S.Mphephu, N.2017-04-202017-02Appadu, AR, Lubuma, J.M-S & Mphephu, N 2017, 'Computational study of three numerical methods for some linear and nonlinear advection-diffusion-reaction problems', Progress in Computational Fluid Dynamics, vol. 17. no. 2, pp. 114-129.1468-4349 (print)1741-5233 (online)10.1504/PCFD.2017.082520http://hdl.handle.net/2263/59995In 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 non-linear 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.en© 2015 Inderscience Enterprises Ltd.Advection-diffusion-reactionStabilityDispersionDissipationFinite differenceUpwind forward Euler schemeNon-standard finite difference (NSFD) schemeUnconditionally positive finite difference (UPFD) schemePostprint Article