In this paper, a parameter‐uniform numerical scheme for the solution of singularly perturbed parabolic convection–diffusion problems with a delay in time defined on a rectangular domain is suggested. The presence of the small diffusion parameter ϵ leads to a parabolic right boundary layer. A collocation method consisting of cubic B‐spline basis functions on an appropriate piecewise‐uniform mesh is used to discretize the system of ordinary differential equations obtained by using Rothe's method on an equidistant mesh in the temporal direction. The parameter‐uniform convergence of the method is shown by establishing the theoretical error bounds. The numerical results of the test problems validate the theoretical error bounds.

中文翻译：

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具有时滞的抛物奇异摄动问题的参数一致格式

本文提出了一个参数一致的数值方案，用于解决在矩形域上定义的具有时间延迟的奇摄动抛物线对流扩散问题。小扩散参数的存在ε通向抛物线右边界层。使用在适当的分段均匀网格上由三次B样条基函数组成的并置方法来离散化在时间方向上等距离网格上使用Rothe方法获得的常微分方程组。通过建立理论误差范围，表明了该方法的参数均匀收敛。测试问题的数值结果验证了理论误差范围。