A numerical process of the mobile-immobile advection-dispersion model arising in solute transport

Document Type : Original Article


1 Department of Mathematics, Faculty of Science, Shahid Rajaee Teacher Training University

2 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 $0< \beta \leq 1$ (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.


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Volume 3, Issue 3
September 2022
Pages 1-10
  • Receive Date: 26 May 2022
  • Revise Date: 14 August 2022
  • Accept Date: 16 August 2022
  • First Publish Date: 01 September 2022