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Numerical solution of the time fractional nonlinear burgers equation using the quintic B-Spline method | ||
| Journal of Mathematical Modeling | ||
| دوره 14، شماره 1، خرداد 2026، صفحه 253-271 اصل مقاله (366.52 K) | ||
| نوع مقاله: Research Article | ||
| شناسه دیجیتال (DOI): 10.22124/jmm.2025.31069.2784 | ||
| نویسندگان | ||
| Fahad Kamil Nashmi* 1؛ Bushra Aziz Taha2 | ||
| 1Department of Mathematics, College of Science, University of Basrah, Basrah, Iraq. | ||
| 2Department of Mathematics, College of Science, University of Basrah, Basrah, Iraq | ||
| چکیده | ||
| This paper introduced a novel approach for resolving fractional partial differential equations. The time fractional nonlinear Burgers equation of order k was solved to illustrate the efficacy of the technique, where k in (0;1]. The quintic B-spline method facilitated spatial partitioning, while the finite difference method addressed the fractional Caputo derivative, which simulates anomalous diffusion processes influenced by memory effects. The proposed methods stability is demonstrated utilizing the von Neumann technique; it has been shown to be unconditionally stable. Additionally, a convergence study is shown, demonstrating that the approach exhibits uniform convergence of (gh4 +s(Dh2)). We validated the methods correctness through numerical tests by comparing it with the exact solution and alternative numerical methods. Based on L2 and L¥ error norms, the quintic B-spline approach exhibits improved convergence rates and reduced computing costs. | ||
| کلیدواژهها | ||
| Quintic B-spline method؛ finite difference techniques؛ Caputo time-fractional derivative؛ Burgers equation | ||
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آمار تعداد مشاهده مقاله: 54 تعداد دریافت فایل اصل مقاله: 125 |
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