一类奇异摄动问题有限差分逼近改进的一致收敛性

摘要

For a kind of singularly perturbed problems, a semi-discretised approximation is investigated, in which the mesh is constructed adaptively by equidistributing the standard arc-length monitor function of the solution. Based on the discrete maximum principle and a priori truncation error estimate, the error of the numerical solution in the dis crete maximum norm is achieved, first-order uniformly convergent with respect to the perturbation parameter ε. Comparing with the existing literature, the error convergence order in the current work has been greatly improved. The experiment is carried out, which coincides with the theorectical analysis.%对于一类奇异摄动问题,给出了一种半离散差分格式,其网格是通过等分布所研究问题解的弧长控制函数而生成的.通过采用离散最大模原理和先验截断误差估计,证明了离散最大模下数值解是关于摄动参数ε一阶一致收敛的.这比已有文献中的误差收敛阶有明显的改进.数值实验验证了理论分析的正确性.