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

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

Document Type : Research Paper

Authors

Jitesh P. Mandaliya ¹
Deelip Kumar ²

¹ Department of Mathematics, Institute of Infrastructure, Technology, Research and Management, Ahmedabad, Gujarat, India.

² Department of Mathematics, Government Post Graduate College Noida, Uttar Pradesh, India.

10.22034/cmde.2025.66680.3142

Abstract

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.

Keywords

Main Subjects

Numerical Analysis

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