A second-order box solver for nonlinear delayed convection-diffusion equations with Neumann boundary conditions

In this paper, by applying order reduction approach, a second-order accurate box scheme is established to solve a nonlinear delayed convection-diffusion equations with Neumann boundary conditions. By the discrete energy method, it is shown that the difference scheme is uniquely solvable, and has a convergence rate of O(∆t² + h²) with respect to L² - norm in constrained and non-constrained temporal grids. Besides, for constrained temporal step, a Richardson extrapolation method (REM) used along with the box scheme, which makes final solution third-order accurate in both time and space, is developed in detail. Finally, numerical results confirm the accuracy and efficiency of our solvers.