%0 Journal Article
%T A numerical process of the mobile-immobile advection-dispersion model arising in solute transport
%J Mathematics and Computational Sciences
%I Qom University of Technology
%Z 2717-2708
%A Esmaeelzade Aghdam, Y
%A Farnam, B
%D 2022
%\ 09/01/2022
%V 3
%N 3
%P 1-10
%! A numerical process of the mobile-immobile advection-dispersion model arising in solute transport
%K Mobile-immobile advection-dispersion model
%K Legendre polynomials
%K stability
%K Convergence
%R 10.30511/mcs.2022.554606.1072
%X In the present article, to find the answer to the mobile-immobile advection-dispersion model of temporal fractional order $0< \beta \leq 1$ (MI-ADM-TF), which can be applied to model the solute forwarding in watershed catchment and flood, the effective high-order numerical process is gonna be built.To do this, the temporal-fractional derivative of the MI-ADM-TF is discretized by using the linear interpolation, and the temporal-first derivative by applying the first-order precision of the finite-difference method. On the other hand, After obtaining a semi-discrete form, to obtain the full-discrete technique, the space derivative is approximated utilizing a collocation approach based on the Legendre basis.The convergence order of the implicit numerical design for MI-ADM-TF is discussed in that is linear.Moreover, the temporal-discretized structure of stability is also discussed theoretically in general in the article.Eventually, two models are offered to demonstrate the quality and authenticity of the established process.
%U http://mcs.qut.ac.ir/article_254908_22acd5f166739af21a07a0042fcac86d.pdf