This article studies a Dirichlet boundary value problem for singularly perturbed time delay convection-diffusion equation with degenerate coefficient. A priori explicit bounds are established on the solution and its derivatives. For asymptotic analysis of the spatial derivatives the solution is decomposed into regular and singular parts. To approximate the solution a numerical method is considered which consists of backward Euler scheme for time discretization on uniform mesh and a combination of midpoint upwind and central difference scheme for the spatial discretization on modified Shishkin mesh. Further, the order of convergence is increased in time direction via implementing Richardson extrapolation. Stability analysis is carried out, numerical results are presented and comparison is done with upwind scheme on uniform mesh as well as upwind scheme on Shishkin mesh to demonstrate the effectiveness of the proposed methods. The convergence obtained in practical satisfies the theoretical predictions.

中文翻译：

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具有退化系数的奇异扰动延迟抛物线对流扩散问题的稳健数值方案

本文研究了具有退化系数的奇摄动时滞对流扩散方程的Dirichlet边值问题。在解及其导数上建立了先验显式界限。对于空间导数的渐近分析，解被分解为规则部分和奇异部分。为了近似求解，考虑了一种数值方法，该方法包括用于均匀网格上的时间离散化的后向欧拉方案和用于改进 Shishkin 网格上的空间离散化的中点逆风和中心差分方案的组合。此外，通过实现理查森外推，在时间方向上增加了收敛的阶数。进行稳定性分析，给出了数值结果，并与均匀网格上的迎风方案和 Shishkin 网格上的迎风方案进行了比较，以证明所提出方法的有效性。实际得到的收敛满足理论预测。