Unconditionally stable high-order scheme for the fractional generalized Burgers-Huxley equation

Iranian Journal of Numerical Analysis and Optimization

مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 27 مرداد 1404

نوع مقاله: Research Article

شناسه دیجیتال (DOI): 10.22067/ijnao.2025.93568.1649

نویسندگان

Mojtaba Hajipour^{* 1}؛ Yashar Lakpour¹؛ Dumitru Baleanu^{2، 3}

¹Department of Mathematics, Sahand University of Technology, P.O. Box: 51335-1996, Tabriz, Iran

²Department of Computer Science and Mathematics, Lebanese American University, Beirut, Lebanon

³Institute of Space Sciences, Magurele, Romania

چکیده

This study presents a high-order numerical scheme for solving the generalized fractional-order Burgers-Huxley equation, a nonlinear evolutionary PDE combining integer-order spatial derivatives with temporal fractional derivatives. The model captures essential features of reaction-diffusion-convection systems and neural pulse propagation dynamics. We develop a fourth-order compact finite difference method for spatial discretization coupled with a Grünwald-Letnikov approximation for the fractional time derivative. The resulting nonlinear system is solved using an efficient iterative algorithm. Rigorous analysis demonstrates that the proposed method is unconditionally stable and achieves $\mathcal{O}(\tau^3 + h^4)$ convergence, where $\tau$ and $h$ represent temporal and spatial step sizes, respectively. Numerical experiments confirm the theoretical results and illustrate the scheme's accuracy through multiple test cases, demonstrating its effectiveness in handling this class of fractional PDEs.

کلیدواژه‌ها

Burgers-Huxley equation؛ Finite difference formula؛ High-order method؛ Stability؛ Iterative method