This article contributes a numerical technique for a class of singularly perturbed time delayed parabolic partial differential equation. A priori results of maximum principle, stability and bounds are discussed. The continuous problem is semi-discretized by the Crank–Nicolson based scheme in the temporal direction and then discretized by the tension spline scheme on non-uniform Shishkin mesh. Error estimation for the discretized problem is derived. To validate the theoretical findings, the numerical outcomes for linear and nonlinear problems are tested.

中文翻译：

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一类时间相关的奇异摄动抛物线偏微分方程的张力样条计算研究

本文为一类奇摄动时滞抛物型偏微分方程提供了数值技术。讨论了最大原理，稳定性和界限的先验结果。连续问题由基于Crank–Nicolson的方案在时间方向上进行半离散，然后由张力样条方案在非均匀的Shishkin网格上离散化。推导了离散问题的误差估计。为了验证理论结果，测试了线性和非线性问题的数值结果。