In this paper, a system of time dependent boundary layer originated reaction dominated problems with diffusion parameters of different magnitudes, is considered for numerical analysis. The presence of these parameters lead to the boundary layer phenomena. Here, an optimal order uniformly accurate boundary layer adaptive method moving mesh method is proposed. This method is able to capture the layer phenomena without using a priori information of the solution. The problem is discretized by a modified implicit-Euler scheme in time direction. For the present system, adaptive mesh generation is required in space due to the singularly perturbed nature of the problem. For this purpose, a positive error monitor function is used whose equidistribution will move the mesh points toward the boundary layers. Parameter uniform error estimates are derived to show that the convergence rate is optimal with respect to the problem discretization. Numerical experiments strongly verify the theoretical findings and confirm the efficiency and accuracy of the proposed method.

在本文中，考虑了一个时变边界层引发的反应控制问题，该系统具有不同幅度的扩散参数，用于数值分析。这些参数的存在导致边界层现象。在此，提出了一种最优阶均匀精确边界层自适应方法移动网格方法。此方法无需使用解决方案的先验信息即可捕获层现象。通过改进的隐式Euler方案在时间方向上离散了该问题。对于本系统，由于问题的奇异摄动性质，需要在空间中生成自适应网格。为此，使用正误差监控器功能，其正向分布将使网格点移向边界层。得出参数统一误差估计值，以表明收敛速度相对于问题离散化而言是最佳的。数值实验强有力地验证了理论发现，并证实了该方法的有效性和准确性。