Appadu, A. RaoDjoko, J.K. (Jules Kamdem)Gidey, H.H.2016-02-192016-01Appadu, AR, Djoko, JK & Gidey, HH 2016, 'A computational study of three numerical methods for some advection-diffusion problems', Applied Mathematics and Computation, vol. 272, part 3, pp. 629-647.0096-3003 (print)1873-5649 (online)10.1016/j.amc.2015.03.101http://hdl.handle.net/2263/51468Three numerical methods have been used to solve two problems described by advection-diffusion equations with specified initial and boundary conditions. The methods used are the third order upwind scheme [4], fourth order upwind scheme [4] and Non-Standard Finite Difference scheme (NSFD) [9]. We considered two test problems. The first test problem has steep boundary layers near x = 1 and this is challenging problem as many schemes are plagued by non-physical oscillation near steep boundaries [15]. Many methods suffer from computational noise when modelling the second test problem especially when the coefficient of diffusivity is very small for instance 0.01. We compute some errors, namely L2 and L1 errors, dissipation and dispersion errors, total variation and the total mean square error for both problems and compare the computational time when the codes are run on a matlab platform. We then use the optimization technique devised by Appadu [1] to find the optimal value of the time step at a given value of the spatial step which minimizes the dispersion error and this is validated by some numerical experiments.en© 2015 Elsevier Inc. All rights reserved. Notice : this is the author’s version of a work that was accepted for publication in Applied Mathematics and Computation. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Applied Mathematics and Computation, vol. 272, pp. 629-647. 2016. doi : 10.1016/j.amc.2015.03.101.DispersionDissipationTotal variationOscillationsAdvection-diffusionOptimizationPostprint Article