In this paper, a coupled system of singularly perturbed parabolic one-dimensional reaction–diffusion equations with discontinuous source terms is considered. To obtain a reliable approximation of the system solution, we construct a numerical method by using an effective finite-difference scheme which involves a suitable layer-adapted piecewise-uniform Shishkin mesh. We show that the approximations provided by the proposed numerical method converge uniformly with respect to the singular perturbation parameter. The performance of the singularly perturbed parabolic system successfully tested illustrates the agreement with the theoretical results.

中文翻译：

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具有不连续源项的奇摄动瞬态反应扩散方程耦合系统的有限差分格式

在本文中，考虑了具有不连续源项的奇异摄动抛物线一维反应-扩散方程的耦合系统。为了获得系统解的可靠近似值，我们通过使用有效的有限差分方案构建了一种数值方法，该方案涉及合适的层适应分段均匀 Shishkin 网格。我们表明，所提出的数值方法提供的近似值关于奇异扰动参数均匀收敛。成功测试的奇异微扰抛物线系统的性能说明了与理论结果的一致性。