This article presents a stable finite difference approach for the numerical approximation of singularly perturbed differential-difference equations (SPDDEs). The proposed scheme is oscillation-free and much accurate than conventional methods on a uniform mesh. Error estimates show that the scheme is linear convergent in space and time variables. By using the Richardson extrapolation technique, the obtained results are extrapolated in order to get better approximations. Some numerical examples are taken from literature to validate the theory, showing good performance of the proposed method.

中文翻译：

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具有位移参数的抛物型奇摄动PDE的稳定有限差分格式和误差估计。

本文提出了一种稳定的有限差分方法，用于奇异摄动微分方程（SPDDE）的数值逼近。所提出的方案是无振荡的，并且在均匀网格上比常规方法精确得多。误差估计表明该方案在空间和时间变量上是线性收敛的。通过使用Richardson外推技术，对获得的结果进行外推，以获得更好的近似值。文献中的一些数值例子验证了该理论，证明了该方法的良好性能。