Second-order time discrete schemes involving the parameter \(\theta \) are proposed and analyzed, in combination with the finite element method (FEM), for the numerical approximation of the solution to a neural field model governed by nonlocal integro-differential equations incorporating both dendritic fibers and somatic layers The spatial discretization employs FEM, while numerical integration handles the nonlocal interactions. The stability of the second-order \(\theta \) schemes within the FEM framework is studied. A priori error estimates in the \(L^2\) norm and the \(H_\xi ^1\) norm are also derived. The theoretical convergence rates predicted by the error analysis are validated through numerical experiments, confirming the effectiveness and feasibility of the proposed schemes.
