求解一维对流方程的四阶紧致差分格式  

A Fourth Order Compact Difference Scheme for Solving the 1D Convection Equation

作　　者：王小妹 陈豫眉 WANG Xiaomei;CHEN Yumei(School of Mathematics and Information, China West Normal University,Nanchong 637009,China;School of Mathematics Education, China West Normal University,Nanchong 637009,China)

机构地区：[1]西华师范大学数学与信息学院,四川南充637009 [2]西华师范大学公共数学学院,四川南充637009

出　　处：《安阳师范学院学报》2022年第2期4-11,共8页Journal of Anyang Normal University

基　　金：国家自然科学基金面上项目(项目编号11971094);四川省科技厅项目(项目编号2017JY0186);西华师范大学英才基金项目(项目编号17YC371)。

摘　　要：文章针对一维对流方程提出了一种具有四阶精度的紧致差分格式。首先对给定空间区域采用一类四阶紧致差分格式离散,将问题简化为求解关于时间的半离散方程式;其次对时间方向采用保持强稳定龙格库塔法,递推求得每一时间层上的数值解;最后通过数值算例验证了格式的精确性与有效性。In this paper,a compact difference scheme with fourth order accuracy is proposed for one-dimensional convection equation.Firstly,a class of fourth-order compact difference scheme is used to discretize the space region given by one-dimensional convection equation,and the problem is simplified to solve the semi-discrete equation about time.Secondly,the strong stability preserving Runge-Kutta method to the time direction is used to obtain the numerical solutions at each time level.Finally,numerical examples are given to verify the accuracy and validity of the scheme.

关 键 词：对流方程 紧致差分格式 保持强稳定龙格库塔法 

分 类 号：O241.82[理学—计算数学]