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

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 [Formula: see text], 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.