A system of singularly perturbed convection-diffusion equations with Robin boundary conditions is considered on the interval \([0,1]\). It is shown that any solution of such a problem can be expressed to a system of first-order singularly perturbed initial value problem, which is discretized by the backward Euler formula on an arbitrary nonuniform mesh. An a posteriori error estimation in maximum norm is derived to design an adaptive grid generation algorithm. Besides, in order to establish the initial values of the original problems, we construct a nonlinear optimization problem, which is solved by the Nelder–Mead simplex method. Numerical results are given to demonstrate the performance of the presented method.

在区间\（[0,1] \）上考虑具有Robin边界条件的奇摄动对流扩散方程组。结果表明，此类问题的任何解决方案都可以表示为一阶奇异摄动初始值问题的系统，该系统由后向欧拉公式在任意不均匀网格上离散化。推导了最大范数的后验误差估计，以设计一种自适应网格生成算法。此外，为了确定原始问题的初始值，我们构造了一个非线性优化问题，可以通过Nelder-Mead单纯形法加以解决。数值结果表明了所提出方法的性能。