《偏微分方程数值解》的算法设计研究——变系数线性对流方程的计算格式  

Algorithm Design and Research on "Numerical Solution of Partial Differential Equations"——Computation Scheme of Variable Coefficient Linear Convection Equations

作　　者：王国栋 闵杰 Wang Guodong;Min Jie(School of Mathematics and Physics,Anhui Jianzhu University,Hefei 230601,China)

机构地区：[1]安徽建筑大学数理学院,安徽合肥230601

出　　处：《黄山学院学报》2018年第3期1-4,共4页Journal of Huangshan University

基　　金：安徽省教育厅教学研究项目(2015jyxm251);安徽建筑大学教育研究项目(2017jy23)

摘　　要：一维线性对流方程是《偏微分方程数值解》中双曲型方程的经典模型,它的计算格式对双曲型偏微分方程的算法设计有重要影响。文章讨论了该方程的一种推广模型,即一维变系数交通流模型方程(仍为线性偏微分方程)的准确解,并将教材中的迎风格式发展运用到该模型,然后利用新的格式模拟相关实例。One-dimensional linear convection equation is a classic model of hyperbolic equation in the numerical solution of partial differential equations.Its numerical schemes have important influence on the numerical methods of hyperbolic partial differential equations.The exact solution for a generalization of the equation,namely one-dimensional variable coefficients traffic flow model equation(still a linear partial differential equation)is discussed,and the upwind scheme in the textbook is applied to compute variable coefficients traffic flow model equations.Furthermore,the new scheme is used to simulate related examples.

关 键 词：线性对流方程 变系数 交通流模型 迎风格式 

分 类 号：O175.27[理学—数学]