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High-accuracy fully discrete schemes for 2D time-space fractional models with nonlinear dynamics | ||
| Computational Methods for Differential Equations | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 16 مهر 1404 اصل مقاله (1.76 M) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22034/cmde.2025.68655.3338 | ||
| نویسندگان | ||
| Safar Irandoust-pakchin* 1؛ Mohammad Hossein Derakhshan1؛ Mohamed Adel* 2 | ||
| 1Department of Applied Mathematics, Faculty of Mathematics, Statistics and Computer Sciences, University of Tabriz, Tabriz, Iran. | ||
| 2Department of Mathematics, Faculty of Science, Islamic University of Madinah, Medina, KSA. | ||
| چکیده | ||
| This paper introduced a fully discrete numerical scheme for solving two-dimensional fractional diffusion equations. The time fractional derivative in the Caputo sense was discretized using a local quadratic polynomial approximation, enhancing accuracy in temporal integration. For spatial fractional derivatives of Riesz type, a nonuniform fractional central difference scheme is developed to effectively handle two-dimensional domains with variable mesh sizes. Stability and convergence analyses confirmed the robustness and precision of the method. Numerical experiments demonstrated that the scheme achieved high-order accuracy in both time and space, validated by exact solutions. The method efficiently managed nonlinear diffusion and reaction terms, showing excellent agreement between numerical and analytical results. Computational performance was evaluated through error norms and CPU time metrics, confirming the methods practical ity for complex fractional models. This approach offered a flexible and accurate tool for modeling anomalous diffusion processes across various scientific and engineering applications. | ||
| کلیدواژهها | ||
| Nonuniform fractional central difference؛ Stability analysis؛ Riesz fractional derivative؛ Local quadratic polynomial | ||
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آمار تعداد مشاهده مقاله: 76 تعداد دریافت فایل اصل مقاله: 100 |
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