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A study of weighted $b$-spline method for solving nonlocal subdiffusion model | ||
| Computational Methods for Differential Equations | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 20 مرداد 1404 اصل مقاله (1.74 M) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22034/cmde.2025.66680.3142 | ||
| نویسندگان | ||
| Jitesh P. Mandaliya* 1؛ Deelip Kumar2 | ||
| 1Department of Mathematics, Institute of Infrastructure, Technology, Research and Management, Ahmedabad, Gujarat, India. | ||
| 2Department of Mathematics, Government Post Graduate College Noida, Uttar Pradesh, India. | ||
| چکیده | ||
| In this study, we employ weighted $b$-splines to obtain the numerical solution for the nonlocal subdiffusion equation widely used in population dynamics. For spatial discretization, we utilize weighted \( b \)-spline method that is computationally efficient, providing accurate results with fewer parameters. The temporal discretization is performed using \( L1 \) and \( L2 \)-\( 1_\sigma \) schemes on a graded mesh. We establish the existence, uniqueness, and regularity of the solution at the continuous level. Furthermore, we derive \emph{a priori} error bounds and convergence estimates in both \( L^2(\Omega) \) and \( H_0^1(\Omega) \) norms using a \( \alpha \)-robust discrete Gronwall inequality. The theoretical findings are validated through three numerical examples. | ||
| کلیدواژه‌ها | ||
| Mesh-free method؛ Weighted $b$-spline؛ $L1$ and $L2$-$1_\sigma$ methods | ||
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آمار تعداد مشاهده مقاله: 62 تعداد دریافت فایل اصل مقاله: 74 |
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