A study of weighted $b$-spline method for solving nonlocal subdiffusion model

Document Type : Research Paper

Authors

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.

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 \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.

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Articles in Press, Accepted Manuscript
Available Online from 11 August 2025
  • Receive Date: 08 April 2025
  • Revise Date: 15 July 2025
  • Accept Date: 08 August 2025