一类非线性变系数Burgers方程初边值问题的差分方法  

The Difference Method for the Initial Boundary Value Problem of a Nonlinear Variable Coefficient Burgers Equations

作　　者：张伟燕 杨雪花 张海湘 石扬 ZHANG Weiyan;YANG Xuehua;ZHANG Haixiang;SHI Yang(College of Science,Hunan University of Technology,Zhuzhou Hunan 412007,China)

机构地区：[1]湖南工业大学理学院,湖南株洲412007

出　　处：《湖南工业大学学报》2025年第5期89-97,共9页Journal of Hunan University of Technology

基　　金：国家自然科学基金资助项目(12226340,12226337,12126321);湖南省自然科学基金资助项目(2022JJ50083);湖南省教育厅优秀青年基金资助项目(21B0550)。

摘　　要：针对一维非线性变系数Burgers方程的初边值问题进行差分方法研究。首先,利用差分方法,建立二层非线性差分格式;然后证明该差分格式在适当的条件下具有稳定性、收敛性;最后,通过具体数值算例,验证了本文构造的差分方法的有效性。算例结果表明该差分格式在空间和时间上都具有2阶精度,展示了其在计算精度、稳定性等方面的优势。An inquiry has been made into the difference method for the initial boundary value problem of one-dimensional nonlinear variable coefficient Burgers equation.Firstly,by using the difference method,a two-layer nonlinear difference scheme has been established,followed by a proof of stability and convergence under appropriate conditions to be possessed by the proposed difference scheme.Finally,the effectiveness of the differential method constructed in this current research can be verified through specific numerical examples.The results indicate that the differential scheme is characterized with second-order accuracy in both space and time,thus demonstrating its advantages in computational accuracy,stability,and other aspects.

关 键 词：计算数学 非线性变系数Burgers方程 二层格式 非线性差分格式 稳定性 收敛性 

分 类 号：O241.3[理学—计算数学]