Research Highlights

Mesh-Free Galerkin Approximation for Coupled Time-Fractional Nonlocal Reaction–Diffusion Problem Using Weighted b-Splines

Authors :- Jitesh P. Mandaliya

Publication :- Iranian Journal of Science, Springer, 2025

In this paper, we study a coupled time-fractional nonlocal reaction–diffusion problem. The nonlocal reaction–diffusion framework is widely used in population dynamics. We discuss the existence and uniqueness of the solution at continuous level. A unified linearized numerical scheme is developed which uses weighted b-splines for spatial direction and L1, L2- schemes for temporal direction. The weighted b-spline based mesh-free method has some advantages over standard finite element method. Moreover, we derive stability estimates and -robust convergence estimates in and norms. The established results are validated through some numerical examples.