KdV-Burgers方程的一类本性并行差分方法

删除或更新信息，请邮件至freekaoyan#163.com(#换成@)

本站小编 Free考研考试/2021-12-27

KdV-Burgers方程的一类本性并行差分方法潘悦悦, 杨晓忠华北电力大学数理学院, 北京 102206 A Class of Difference Method with Intrinsic Parallelism for Kdv-Burgers Equation PAN Yueyue, YANG XiaozhongSchool of Mathematics and Physics, North China Electric Power University, Beijing 102206, China

摘要
图/表
参考文献
相关文章(3)
点击分布统计
下载分布统计
-->

全文: PDF(659 KB) HTML (1 KB)
输出: BibTeX | EndNote (RIS)

摘要KdV-Burgers方程是非线性耗散和色散型波动方程，可以作为湍流规范方程，具有广泛的物理背景，其数值解法具有重要的科学意义和实际应用价值.针对KdV-Burgers方程，本文结合经典Crank-Nicolson格式和四个不同类型的Saul'yev非对称格式，提出了一类本性并行差分方法，构造交替分段Crank-Nicolson （ASC-N）差分格式.分析证明了ASC-N格式解的存在唯一性，线性绝对稳定性和计算精度.理论分析和数值试验结果均表明ASC-N差分格式线性绝对稳定，具有空间2阶精度，时间2阶精度（除内边界点外）.在计算效率上，ASC-N格式具有明显的并行计算性质，相比较于隐式格式大幅度节省了计算时间.表明本文方法求解KdV-Burgers方程是高效可行的.

服务

加入引用管理器

E-mail Alert

RSS

收稿日期: 2018-08-02

PACS:

O241.8

基金资助:国家自然科学基金（No.11371135），国家科技重大专项基金（No.2017ZX07101001-01）资助项目.

引用本文:

潘悦悦, 杨晓忠. KdV-Burgers方程的一类本性并行差分方法[J]. 应用数学学报, 2019, 42(5): 577-594. PAN Yueyue, YANG Xiaozhong. A Class of Difference Method with Intrinsic Parallelism for Kdv-Burgers Equation. Acta Mathematicae Applicatae Sinica, 2019, 42(5): 577-594.

链接本文:

http://123.57.41.99/jweb_yysxxb/CN/或 http://123.57.41.99/jweb_yysxxb/CN/Y2019/V42/I5/577

[1]	程建春. 数学物理方程及其近似方法(第二版). 北京:科学出版社, 2017 (Cheng J C. Mathematical physics equation and its approximate method (Second Edition). Beijing:Science Press, 2017)
[2]	李志斌. 非线性数学物理方程的行波解. 北京:科学出版社, 2007 (Li Z B. Traveling Wave Solutions of Nonlinear Mathematical Physical Equations. Beijing:Science Press, 2007)
[3]	刘式达, 刘式适. 湍流的KdV-Burgers方程模型. 中国科学 (A辑), 1991, 21(9):938-946 (Liu S D, Liu S S. The Model of Turbulent KdV-Burgers Equation. Science in China (Series A), 1991, 21(9):938-946)
[4]	Liu S K, Liu S D. Heteroclinic Orbit on the KdV-Burgers Equation and Fisher Equation. Commun. Theor. Phys., 1991. 16(4):497-500
[5]	Evans D J, Abdullah A R B. Group explicit methods for parabolic equations. Intern. J. Computer Math., 1983, 14(1):73-105
[6]	Zhang B L, Li W Z. On Alternating Segment Crank-Nicolson Scheme. Parallel Comput., 1994, 20(6):897-902
[7]	张宝琳, 袁国兴, 刘兴平等. 偏微分方程并行有限差分方法. 北京:科学出版社, 1994 (Zhang B L, Yuan G X, Liu X P, etc. Parallel finite difference methods for partial differential equations. Beijing:Science Press, 1994)
[8]	张宝琳, 谷同祥, 莫则尧. 数值并行计算原理与方法. 北京:国防工业出版社, 1999 (Zhang B L, Gu T X, Mo Z Y. The Principle and Method of Numerical Parallel Computing. Beijing:National Defense Industry Press, 1999)
[9]	周毓麟. 拟线性抛物组具有并行本性的差分格式. 中国科学 (A辑), 1997, 27(1):43-48 (Zhou Y L. Difference Schemes with Parallelism Intrinsic for Quasilinear Parabolic Systems. Science in China (Series A), 1997, 27(1):43-48)
[10]	Biorstad P, Luskin M. Parallel Solution of Partial Differential Equations. New York:Springer-Verlag, 2000
[11]	Yang X Z, Wu L F, Shi Y Y, A new kind of parallel finite difference method for the quanto option pricing model. Advances in Difference Equations, (2015) 2015:311, DOI:10.1186/s13662-015-0643-z
[12]	朱少红, 袁光伟. 色散方程的一类本性并行的差分格式. 应用数学学报, 2003, 26(3):495-503 (Zhu S H, Yuan G W. Difference Scheme with Intrinsic Parallelism for Dispersive Equation. Acta Mathematicae Applicatae Sinica, 2003, 26(3):495-503)
[13]	王廷春, 张鲁明. 求解Burgers方程的一种交替分段隐式算法. 计算物理, 2005, 22(2):137-142 (Wang T C, Zhang L M. An Alternating Segment Implicit Method for Burgers Equations. Chinese Journal of Computational Physics, 2005, 22(2):137-142)
[14]	王文洽. KdV方程的一类本性并行差分格式. 应用数学学报, 2006, 29(6):995-1003 (Wang W Q. Difference Schemes with Intrinsic Parallelism for the KdV Equation. Acta Mathematicae Applicatae Sinica, 2006, 29(6):995-1003)
[15]	袁光伟, 盛志强等. 扩散方程计算方法. 北京:科学出版社, 2015 (Yuan G W, Sheng Z Q, etc. Calculation method of diffusion equation. Beijing:Science Press, 2015)
[16]	张强. 偏微分方程的有限差分方法. 北京:科学出版社, 2017 (Zhang Q. Finite Difference Methods for Partial Differential Equations. Beijing:Science Press, 2017)
[17]	Kaya D. An application of the decomposition method for the KdVB equation. Appl. Math. Comput., 2004, 152(1):279-288
[18]	Darvishi M T, Khani F, Kheybari S. A numerical solution of the KdV-Burgers'equation by spectral collocation method and Darvishi's preconditionings. Int. J. Contemp. Math. Sciences, 2007, 2(22):1085-1095
[19]	Vong S, Lyu P, Wang Z B. A compact difference scheme for fractional sub-diffusion equations with the spatially variable coefficient under neumann boundary conditions. Journal of Scientific Computing, 2016, 66(2):725-739
[20]	Gao G H, Sun Z Z. Two difference schemes for solving the one-dimensional time distributed-order fractional wave equations. Numerical Algorithms, 2017, 74(3):675-697
[21]	迟学斌, 王彦棢, 王珏等. 并行计算与实现技术. 北京:科学出版社, 2015 (Chi X B, Wang Y W, Wang J, etc. Parallel Computing and Implementation Technology. Beijing:Science Press, 2015)
[22]	刘维. 实战Matlab之并行程序设计. 北京:北京航空航天大学出版社, 2012 (Liu W. Practical Parallel Programming of Matlab. Beijing:Beihang University Press, 2012)

[1]	杨晓忠, 邵京, 孙淑珍. 双项时间分数阶慢扩散方程的一类高效差分方法[J]. 应用数学学报, 2019, 42(4): 492-505.
[2]	朱少红, 袁光伟. 色散方程的一类本性并行的差分格式[J]. 应用数学学报(英文版), 2003, 26(3): 495-503.
[3]	宣培才, 周定轩. Baskakov算子加权逼近的收敛阶[J]. 应用数学学报(英文版), 1995, 18(1): 129-139.

PDF全文下载地址:

http://123.57.41.99/jweb_yysxxb/CN/article/downloadArticleFile.do?attachType=PDF&id=14651