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Advancing the Solution of Time-Fractional Convection-Diffusion-Reaction Equations with Application to Mobile-Immobile System | ||
| Computational Methods for Differential Equations | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 06 آبان 1405 اصل مقاله (4.79 M) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22034/cmde.2026.70766.3534 | ||
| نویسندگان | ||
| Anthony Anya Okeke* 1؛ Nur Nadiah Abd Hamid2؛ Wen Eng Ong3؛ Buba Musa Tunga Hambagda4؛ Pius Tumba4 | ||
| 11. School of Mathematical Sciences, Universiti Sains Malaysia, 11800 Penang, Malaysia. 2. Department of Mathematics, Federal University Gashua, P.M.B. 1005 Gashua, Yobe State, Nigeria. | ||
| 2Nur Nadiah Academic Services, 13800 Butterworth, Penang, Malaysia. | ||
| 3School of Mathematical Sciences, Universiti Sains Malaysia, 11800 Penang, Malaysia. | ||
| 4Department of Mathematics, Federal University Gashua, P.M.B. 1005 Gashua, Yobe State, Nigeria. | ||
| چکیده | ||
| This paper introduces a novel numerical scheme that integrates cubic B-spline basis functions with the Crank-Nicolson finite difference method to solve the time-fractional convection-diffusion-reaction equation (TFCDRE). The temporal discretization is performed using the $L1$ approximation, while CBS basis functions are employed for spatial discretization. A von Neumann stability analysis establishes the unconditional stability of the proposed scheme for the corresponding constant-coefficient problem. The convergence analysis predicts second-order accuracy in space and $(2-\beta)$-order accuracy in time. The accuracy and effectiveness of the method are demonstrated through several benchmark examples involving both constant and variable coefficients. Numerical results show excellent agreement with exact solutions and confirm the theoretical convergence rates through maximum and Euclidean error norms. Comprehensive graphical investigations, including two-dimensional, three-dimensional, contour, and error plots, further validate the stability and accuracy of the proposed approach. To illustrate its practical applicability, the method is applied to a fractional mobile-immobile transport model, where numerical simulations, parameter studies, and convergence analyses demonstrate its capability to accurately capture anomalous transport dynamics. All computations are carried out using Wolfram Mathematica 14.3. The proposed CBS framework provides an accurate, stable, and computationally efficient tool for solving TFCDREs arising in | ||
| کلیدواژه‌ها | ||
| Time fractional convection-diffusion-reaction equation؛ Caputo fractional derivative؛ Crank-Nicolson finite difference formulation؛ Cubic B-spline functions؛ Stability and convergence | ||
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آمار تعداد مشاهده مقاله: 3 تعداد دریافت فایل اصل مقاله: 4 |
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