湖南工业大学学报2025，Vol.39Issue(5)：89-97,9.DOI:10.3969/j.issn.1673-9833.2025.05.013
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
摘要
Abstract
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Key words
computational mathematics/nonlinear variable coefficient Burgers equation/two-level difference scheme/nonlinear difference scheme/stability/convergence分类
数学引用本文复制引用
张伟燕,杨雪花,张海湘,石扬..一类非线性变系数Burgers方程初边值问题的差分方法[J].湖南工业大学学报,2025,39(5):89-97,9.基金项目
国家自然科学基金资助项目(12226340,12226337,12126321) （12226340,12226337,12126321）
湖南省自然科学基金资助项目(2022JJ50083) （2022JJ50083）
湖南省教育厅优秀青年基金资助项目(21B0550) （21B0550）
