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 ( τ 2 + h x 4 + h y 4 ) with respect to H 1 - and L 2 -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. [ABSTRACT FROM AUTHOR]