Yones Esmaeelzade Aghdam - Department of Mathematics, Faculty of Science, Shahid Rajaee Teacher Training University
Behnaz Farnam - Department of Mathematics, Qom University of Technology, Qom, Iran

In the present article‎, ‎to find the answer to the mobile-immobile advection-dispersion model of temporal fractional order ۰< \beta \leq ۱ (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.

Mobile-immobile advection-dispersion model, Legendre polynomials, stability, Convergence