奇异摄动对流扩散方程组的参数一致的二阶有限差分格式  

A Parameter-uniform Second Order Finite Difference Scheme for a System of Singularly Perturbed Convection-Diffusion Equations

作　　者：廖仪戈 刘利斌 隆广庆 LIAO Yige;LIU Libin;LONG Guangqing(School of Mathematics and Statistics,Nanning Normal University,Nanning 530100,China)

机构地区：[1]南宁师范大学数学与统计学院,广西南宁530100

出　　处：《应用数学》2023年第2期364-376,共13页Mathematica Applicata

基　　金：中央引导地方科技发展资金项目(桂科AD20238065);广西自然科学基金(2018GXNSFDA050014);广西自然科学基金(2020GXNSFAA159010);国家自然科学基金(12261062)。

摘　　要：针对一类奇异摄动对流扩散方程组,在Vulanovic-Bakhvalov网格上构造了经典的迎风有限差分格式,并利用闸函数方法证明了数值方法为一阶收敛.在此基础上,设计了一个Richardson外推格式,并严格证明了外推方法的精度为二阶一致收敛.数值实验验证了本文的理论结果.For a system of singularly perturbed convection-diffusion equations,a classical upwind finite difference scheme is constructed on Vulanovic-Bakhvalov meshes,and the first-order convergence of our proposed numerical method is proved by using barrier-function approach.Furthermore,the Richardson extrapolation scheme is designed.It is shown that the accuracy of the extrapolation method is second-order uniform convergence.The theoretical results are verified by some numerical experiments.

关 键 词：奇异摄动 Vulanovc-Bakhvalov网格 有限差分方法 RICHARDSON外推 

分 类 号：O241.8[理学—计算数学]