مهناز يوسفي

In this study, a new numerical algorithm is presented to solve the fractional time convection-diffusion equation. This algorithm is designed based on a combination of spectral methods an‎d sparse operational matrices. The use of sparse matrices improves the accuracy of the calculation while reducing computational costs. Error an‎d convergence analysis of the proposed method show its better performance compared to existing methods. To eva‎luate the efficiency of the proposed algorithm, it has been used to solve a mathematical model related to the dynamic behavior of the HTLV-I virus. This virus has complex interactions with the immune system. Accurate modeling of these interactions is essential for a deeper understan‎ding of pathogenesis an‎d the development of effective therapeutic strategies. Fractional models are a suitable tool for modeling the dynamics of this virus due to their ability to describe phenomena with memory. Numerical results obtained from numerical simulations of the fractional model of HTLV-I confirm the high efficiency an‎d accuracy of this algorithm in modeling biological phenomena.

معادله انتشار-همرفت، , مشتق كسري , روش هاي طيفي , ماتريس عملياتي تُنُك , ويروس اچ تي ال-1

Convection-diffusion equation , Fractional derivetive , Spectral methods , Sparse Operational matrix , HTLV-I virus

Mahnaz Yousefi

Jalil Rashidinia-Mahboubeh Molavi-Arabshahi