湖南工业大学学报2024，Vol.38Issue(1)：98-104,7.DOI:10.3969/j.issn.1673-9833.2024.01.014
一类非线性Burgers型问题的预测校正紧差分方法
A Predictor-Corrector Compact Difference Scheme for a Class of Nonlinear Burgers Equations
摘要
Abstract
A predictor-corrector compact difference scheme is proposed for a solution of a class of nonlinear Burgers type equations.Firstly,by using the first-order Euler scheme for the first-order time derivative,the time integral term is discretized based on the first-order convolutional quadrature formula,with the two-step prediction correction acheme of the MacCormack method adopted to handle the nonlinear term.Then,a fourth order compact difference is used for the separation of the first and second derivatives of the scattered space,thus construting an Euler prediction correction compact difference fully discrete scheme.Finally,the validity of the proposed algorithm is to be verified by numerical examples.关键词
计算数学/非线性Burgers方程/预测-校正算法/紧差分方法Key words
computational mathematics/nonlinear Burgers equations/predictor-corrector algorithm/compact difference scheme分类
数理科学引用本文复制引用
王佳威,张海湘,杨雪花..一类非线性Burgers型问题的预测校正紧差分方法[J].湖南工业大学学报,2024,38(1):98-104,7.基金项目
国家自然科学基金数学天元基金资助项目(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）
