A CONVERGENCE ANALYSIS OF THE MOBILE–IMMOBILE ADVECTION–DISPERSION MODEL OF TEMPORAL FRACTIONAL ORDER ARISING IN WATERSHED CATCHMENTS AND RIVERS

Hossein Jafari, Yones Esmaeelzade Aghdam, Behnaz Farnam, Nguyen van Thinh and Mantepu Tshepo Masetshaba
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Hossein Jafari: Department of Mathematical Sciences, University of South Africa, UNISA0003, South Africa†Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 110122, Taiwan
Yones Esmaeelzade Aghdam: ��Department of Mathematics, Faculty of Science, Shahid Rajaee Teacher Training University, Tehran 16785-136, Iran
Behnaz Farnam: �Department of Mathematics, Faculty of Science, Qom University of Technology, Qom, Iran
Nguyen van Thinh: �Department of Civil and Environmental Engineering, Seoul National University, Seoul, South Korea
Mantepu Tshepo Masetshaba: ��Department of Decision Sciences, University of South Africa, UNISA0003, South Africa

FRACTALS (fractals), 2023, vol. 31, issue 04, 1-10

Abstract: An efficient high-order computational procedure is going to be created in this paper to determine the solution to the mobile–immobile advection–dispersion model (MIAD) of temporal fractional order 0 < α ≤ 1, which can be employed to model the solute forwarding in watershed catchments and floods. To do it, the temporal-first derivative of MIAD is discretized by using the finite-difference technique’s first-order precision and the linear interpolation’s temporal-fractional derivative. On either side, the space derivative is simulated using a collocation approach based on the Legendre basis to generate the full-discrete method. The order of MIAD-convergence for the implicit numerical structure is explained. Additionally, a basic conceptual discussion of the temporal-discretized stability mechanism is included in this paper. Finally, two models are provided to show the reliability and excellence of the organized approach.

Keywords: Mobile–immobile Advection–dispersion Model; Legendre Polynomials; Stability; Convergence (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1142/S0218348X23400686

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