This work aims at obtaining a numerical approximation to the solution of a two-parameter singularly perturbed convection-diffusion-reaction system of partial differential equations with discontinuous coefficients. This discontinuity, together with small values of the perturbation parameters, causes interior and boundary layers to appear in the solution. To obtain appropriate point-wise accuracy, we have considered a central finite-difference approach in the space variable which is defined on a piecewise uniform Shishkin mesh and an implicit Euler scheme in the temporal variable defined on a uniform mesh. Some computational experiments have been performed, which confirm the theoretical findings.

这项工作旨在获得具有不连续系数的偏微分方程的双参数奇异摄动对流-扩散-反应系统的解的数值近似。这种不连续性与较小的扰动参数值一起导致内部层和边界层出现在解中。为了获得适当的逐点精度，我们考虑了在分段均匀 Shishkin 网格上定义的空间变量中的中心有限差分方法和在均匀网格上定义的时间变量中的隐式欧拉方案。已经进行了一些计算实验，证实了理论发现。