East Asian J. Appl. Math., 8 (2018), pp. 809-833.
Published online: 2018-10
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A numerical method for the generalised second grade fluid through porous media with anomalous diffusion is considered. The method is based on a combination of finite differences in time and a spectral method in space directions. The convergence of the method is rigorously proved and theoretical error estimates are established. The numerical scheme is unconditionally stable and provides a high accuracy if the solution is smooth enough. The results of numerical simulations are consistent with theoretical findings.
}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.0704218.070518 }, url = {http://global-sci.org/intro/article_detail/eajam/12820.html} }A numerical method for the generalised second grade fluid through porous media with anomalous diffusion is considered. The method is based on a combination of finite differences in time and a spectral method in space directions. The convergence of the method is rigorously proved and theoretical error estimates are established. The numerical scheme is unconditionally stable and provides a high accuracy if the solution is smooth enough. The results of numerical simulations are consistent with theoretical findings.