对流占优扩散反应方程的定制有限点法  

Tailored finite point method for convection-dominated diffusion reaction equation

作　　者：杨红红 秦新强[1] YANG Honghong;QIN Xinqiang(School of Science,Xi＇an University of Technology,Xi＇an 710054,China)

机构地区：[1]西安理工大学理学院,陕西西安710054

出　　处：《西安理工大学学报》2018年第2期211-215,222,共6页Journal of Xi'an University of Technology

基　　金：国家自然科学基金资助项目(51409212)

摘　　要：传统的微分方程数值解方法求解对流占优扩散反应方程时,往往产生数值震荡现象。为了消除数值震荡,本文结合定制有限点方法(TFPM)构造了一种新的数值算法。该方法基于所求解问题的局部性质量身构建,能够有效消除对流占优引起的数值不稳定。给出了不同离散形式的稳定性条件,并通过数值算例验证了解法的高效性。Using traditional numerical methods to solve convection dominated diffusion reaction equations always causes the phenomenon of numerical oscillations.To eliminate the numerical oscillations,a new method is established by combining the tailored finite point method（TFPM）in this paper.The TFPM has been tailored based on the local properties of the solved problem,effectively eliminating the numerical instability caused by convection dominance.The stability conditions of different discrete forms are given,and TFPM is highly efficient through the verification of numerical examples.

关 键 词：定制有限点法 对流占优扩散反应方程 指数基函数 三角基函数 

分 类 号：O241.82[理学—计算数学]