A class of singularly perturbed parabolic delay differential equation with discontinuous data is solved numerically. Numerical scheme based on the upwind finite difference method is presented on a specially generated mesh. The proposed numerical method has been analysed for consistency, stability, and convergence. It is found that the method proposed is unconditionally stable, and the convergence obtained is parameter uniform. Numerical illustrations are presented to demonstrate the effectiveness of the technique.

中文翻译：

---

具有不连续系数和内层的抛物线延迟微分方程的自适应差分格式

数值求解一类具有不连续数据的奇摄动抛物线延迟微分方程。在特殊生成的网格上提出了基于迎风有限差分法的数值方案。已对所提出的数值方法的一致性、稳定性和收敛性进行了分析。发现所提出的方法是无条件稳定的，并且得到的收敛是参数一致的。提供了数值插图来证明该技术的有效性。