A study of weighted B-spline method for solving nonlocal sub diffusion model

Mandaliya, Jitesh P.; Kumar, Deelip

doi:10.22034/cmde.2025.66680.3142

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	A study of weighted B-spline method for solving nonlocal sub diffusion model
Computational Methods for Differential Equations
مقاله 1، دوره 14، شماره 4، دی 2026، صفحه 1526-1545 اصل مقاله (978.9 K)
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 {a priori} error bounds and convergence estimates in both $ L^2(\Omega) $ and $ H_0^1(\Omega) $ norms using an $ \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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A study of weighted B-spline method for solving nonlocal sub diffusion model