Journal
APPLIED MATHEMATICS AND COMPUTATION
Volume 272, Issue -, Pages 629-647Publisher
ELSEVIER SCIENCE INC
DOI: 10.1016/j.amc.2015.03.101
Keywords
Dispersion; Dissipation; Total variation; Oscillations; Advection-diffusion optimization
Categories
Funding
- Research Development Programme of the University of Pretoria
- DST/NRF SARChI Chair in Mathematical Models and Methods in Bioengineering and Biosciences
- University of Pretoria, African Institute for Mathematical Sciences (AIMS)-South Africa and Aksum University (Ethiopia)
- [N00 401]
- [85796]
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Three numerical methods have been used to solve two problems described by advectiondiffusion equations with specified initial and boundary conditions. The methods used are the third order upwind scheme [5], fourth order upwind scheme [5] and non-standard finite difference scheme (WC)) [10]. We considered two test problems. The first test problem we considered has steep boundary layers near x = 1 and this is challenging problem as many schemes are plagued by non-physical oscillation near steep boundaries [16]. Many methods suffer from computational noise when modeling the second test problem. We compute some errors, namely 1.2 and 1.-1 errors, dissipation and dispersion errors, total variation and the total mean square error for both problems. We then use an optimization technique [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 numerical experiments. (C) 2015 Elsevier Inc. All rights reserved.
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