基于MATLAB对一维奇异摄动方程高精度格式的研究  

Research on One-dimensional Singular Perturbation Equation High Precision Scheme Based on MATLAB

作　　者：潘轶航 PAN Yihang(School of Mathematics and Information Science,North Minzu University,Yinchuan 750021,China)

机构地区：[1]北方民族大学数学与信息科学学院,宁夏银川750021

出　　处：《现代信息科技》2024年第2期102-107,113,共7页Modern Information Technology

基　　金：宁夏回族自治区大学生创新项目(S2022-11407-036)。

摘　　要：为研究更加精确的求解奇异摄动方程数值解的解法,文章研究传统中心差分格式,迎风格式以及高阶精度格式这三种数值求解格式,使用MATLAB软件进行求解一维奇异摄动对流扩散方程的算例并可视化,对不同方法下求解方程的结果进行了对比和研究,通过对数值算例求解结果的分析,发现在任意网格下,当摄动参数趋于0时,高阶精度格式下解的精度和稳定性较传统的求解格式有显著提升,使在求解奇异摄动方程的方法选择上更具有针对性。In order to study a more accurate numerical solution of singular perturbation equation,this paper studies three numerical solutions of traditional central difference scheme,upwind scheme and high order precision scheme.It uses MATLAB software to solve the one-dimensional singularly perturbed convection-diffusion equations for example and visualization,compares and studies the results of solving equations with different methods.Through the analysis of the results of numerical examples,it is found that under any grid,when the perturbation parameter approaches 0,the accuracy and stability of solution with high order precision scheme are significantly improved compared with traditional solution schemes,which makes the method selection of solving singular perturbation equation be more targeted.

关 键 词：奇异摄动方程 对流扩散方程 MATLAB 高精度格式 

分 类 号：TP391[自动化与计算机技术—计算机应用技术] O241.82[自动化与计算机技术—计算机科学与技术]