A two-grid temporal second-order scheme for the two-dimensional nonlinear Volterra integro-differential equation with weakly singular kernel

A two-grid temporal second-order scheme for the two-dimensional nonlinear Volterra integro-differential equation with a weakly singular kernel is of concern in this paper. The targeted to reduce computation time and improve accuracy developed by Xu et al. (Appl Numer Math 152:169–184, 2020). constructed armed three steps: First, small system solved on coarse grid using fix-point iteration. Second, Lagrange’s linear interpolation formula used arrive at some auxiliary values analysis fine grid. Finally, linearized Crank–Nicolson finite difference Moreover, algorithm uses central approximation spatial derivatives. In direction, derivative integral term are approximated technique product rule, respectively. By means discrete energy method, stability space-time convergence proposed approach obtained $$L^2$$ -norm. numerical verification fulfilled as results given experiments agree theoretical verify effectiveness algorithm.