The high-order multistep ADI solver for two-dimensional nonlinear delayed reaction-diffusion equations with variable coefficients

In this paper, a high-order compact multistep alternating direction implicit (ADI) difference scheme is constructed and analyzed for two-dimensional (2D) nonlinear delayed reaction-diffusion equations (NDREs) with variable coefficients. By the discrete energy method, it is presented that it achieves the convergence rate of O(τ2+hx4+hy4) with respect to H1- and L2-norms in non-constrained temporal grids, and is unconditionally stable. Finally, numerical results demonstrate the effectiveness of our ADI solver and exhibit the correctness of theoretical results.