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

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  \( L۱ \) and \( L۲ \)-\( ۱_\sigma \) 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 \( L^۲(\Omega) \) and \( H_۰^۱(\Omega) \) norms using an \( \alpha \)-robust discrete Gronwall inequality.  The theoretical findings are validated through three numerical examples.

کلیدواژه ها:

Mesh-free method ، Weighted b-spline ، L۱ and L۲-۱_\sigma methods