In this study, we consider the time-delayed singularly perturbed parabolic PDEs (SPPPDEs). We know that the classical finite difference scheme will not produce good results for singular perturbation problems on a uniform mesh. Here, we propose a new stable finite difference (NSFD) scheme, which produces good results on a uniform mesh and also on an adaptive mesh. The NSFD scheme is constructed based on the stability of the analytical solution. Results are compared with the results available in the literature and observed that the proposed method is efficient over the existing methods for solving SPPPDEs.

中文翻译：

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时滞奇摄动抛物PDE的一种新的稳定有限差分格式及其收敛性

在这项研究中，我们考虑了时滞奇摄动的抛物线形PDE（SPPPDE）。我们知道经典的有限差分方案对于均匀网格上的奇异摄动问题不会产生好的结果。在这里，我们提出了一种新的稳定有限差分（NSFD）方案，该方案可以在均匀网格和自适应网格上产生良好的结果。NSFD方案是基于分析解决方案的稳定性构建的。将结果与文献中的结果进行比较，发现所提出的方法比现有的解决SPPPDEs的方法更有效。