On the effectiveness and precision of BDF2-discontinuous Galerkin scheme for nonlinear nonlocal reaction–diffusion models
摘要
This article examines the convergence of the two-step backward difference formula (BDF2)-discontinuous Galerkin (DG) scheme in the context of a nonlocal reaction–diffusion equation. Our methodology integrates BDF2 for temporal discretization with a DG finite element method for spatial discretization, enabling a comprehensive analysis of the nonlocal diffusion equation. We establish optimal-order convergence rates for the fully discrete system. To assess the effectiveness and precision of the proposed scheme, we provide numerical simulations alongside convergence results.