KdV-Burgers方程的一类新本性并行差分格式  

A New Class of Difference Schemes With Intrinsic Parallelism for the KdV⁃Burgers Equation

作　　者：潘悦悦 杨晓忠[2] PAN Yueyue;YANG Xiaozhong(School of Control and Computer Engineering,North China Electric Power University,Beijing 102206,P.R.China;Institute of Information and Computing,School of Mathematics and Physics,North China Electric Power University,Beijing 102206,P.R.China)

机构地区：[1]华北电力大学控制与计算机工程学院,北京102206 [2]华北电力大学数理学院信息与计算研究所,北京102206

出　　处：《应用数学和力学》2023年第5期583-594,共12页Applied Mathematics and Mechanics

基　　金：国家自然科学基金项目(11371135)。

摘　　要：KdV-Burgers方程作为湍流规范方程,具有深刻的物理背景,其快速数值解法具有重要的实际应用价值.针对KdV-Burgers方程,提出了一种新型的并行差分格式.基于交替分段技术,结合经典Crank-Nicolson(C-N)格式、显格式和隐格式,构造了混合交替分段Crank-Nicolson(MASC-N)差分格式.理论分析表明MASC-N格式是唯一可解、线性绝对稳定和二阶收敛的.数值试验表明,MASC-N格式比C-N格式具有更高的精度和效率.与ASE-I和ASC-N差分格式相比,MASC-N并行差分格式有最好的性能.表明该文的MASC-N并行差分方法能有效地求解KdV-Burgers方程.The KdV⁃Burgers equation as a standard equation for turbulent,has a profound physical background and its fast numerical methods are of great practical application value.A new class of parallel difference schemes were proposed for the KdV⁃Burgers equation.Based on the alternating segment technology,the mixed alternating segment Crank⁃Nicolson(MASC⁃N)difference scheme was constructed with the classic Crank⁃Ni⁃colson(C⁃N)scheme,the explicit and implicit schemes.The theoretical analyses indicate that,the MASC⁃N scheme is uniquely solvable,linearly absolutely stable and 2nd⁃order convergent.Numerical experiments show that,the MASC⁃N scheme has higher precision and efficiency than the C⁃N scheme.Compared with the ASE⁃I and ASC⁃N difference schemes,the MASC⁃N parallel difference scheme has the best performance,and can ef⁃fectively solve the KdV⁃Burgers equation.

关 键 词：KDV-BURGERS方程 MASC-N并行差分格式 线性绝对稳定性 收敛性 数值试验 

分 类 号：O241.8[理学—计算数学]