一类奇异摄动问题时间独立的反应扩散方程的半离散方法（英文）  

A Semi-discrete Method for Solving a Singularly Perturbed Time-dependent Reaction-diffusion Problem

作　　者：上官珍萍 隆广庆 刘利斌 

机构地区：[1]广西师范学院数学与统计科学学院,广西南宁530023

出　　处：《广西师范学院学报（自然科学版）》2017年第4期1-8,共8页Journal of Guangxi Teachers Education University(Natural Science Edition)

基　　金：supported by National Science Foundation of China(11461011,11761015);Natural Science Foundation of Guangxi Education Department(ZD2014080)

摘　　要：该文主要考虑一类奇异摄动时间独立的反应扩散方程的数值方法.对于空间方向的离散,采用在分片均匀的Shishkin网格上的迎风有限差分策略.而对于时间的离散,采用在均匀网格上的高精度半离散方法.稳定性分析表明此格式是绝对稳定的.同时,为了得到最优的Shishkin网格,该文将Shishkin网格参数选择问题转化为一个非线性无约束优化问题,然后利用单纯形算法求解.数值结果表明了该方法的有效性.同时需要指出的是,通过单纯形算法得到的最优网格参数提高了在边界层处的数值解的精度.In this paper, the numerical method of a singularly perturbed timc-dcpcndcnt reaction-diffusion prob-lem that arises from chemical reactor theory is under consideration. T＇hc presented numericupwind finite difference scheme on a picccwise-uniform Shishkin mesh for the spatial discretization and a high accu-racy semi-discrete method on a uniform mesh for the time discretization. It is also shown is unconditionally stable.Then, to obtain an optimal Shishkin mesh,we transform the Shishkin lection problem into a nonlinear unconstrained optimization problem which is solved by using the Ncldcr-Mcad sim-plex algorithm. Numerical results are presented to demonstrate the efficiency of the presented methods, tt should bepointed out that the accuracy of numerical solution on the boundary layers is improvesimplex algorithm to optimize Shishkin mesh parameter.

关 键 词：奇异摄动 半离散方法 SHISHKIN网格 单纯形算法 

分 类 号：O175.2[理学—数学]