In this paper, an efficient splitting domain decomposition method scheme for solving time-dependent convection–diffusion reaction equations is analyzed. A three-step method along each direction is used to solve the solution over each block-divided sub-domain at every time interval. The new solutions are firstly solved by the quadratic interpolation. Then, the intermediate fluxes on the interfaces of sub-domains are computed by local multi-point weighted average from the new solutions. Lastly, the solutions and fluxes in the interiors of sub-domains are computed by the splitting implicit characteristic difference method. By some auxiliary lemmas and the defined intermediate exact solution, the stability and error estimate are given in discrete $L^2$-norm. We further prove that our scheme is of second-order convergence in space and of first-order convergence in time. Numerical experiments are presented to validate theoretical result.

在本文中，分析了一种有效的分裂域分解方法方案，用于求解与时间有关的对流扩散反应方程。沿着每个方向的三步方法用于在每个时间间隔内对每个块划分的子域进行求解。新的解决方案首先通过二次插值解决。然后，通过新解的局部多点加权平均计算出子域界面上的中间通量。最后，利用分裂隐式特征差分法计算了子域内部的解和通量。通过一些辅助引理和定义的中间精确解，可以给出离散的稳定性和误差估计${\mathrm{大号}}^2$-规范。我们进一步证明我们的方案是空间的二阶收敛和时间的一阶收敛。通过数值实验验证了理论结果。