兰州大学机构库 >数学与统计学院
关于Petrov-Galerkin谱方法的两个问题研究
Alternative TitleResearch on Petrov-Galerkin Spectral method for two problems
赵晓丹
Thesis Advisor伍渝江
2009-05-30
Degree Grantor兰州大学
Place of Conferral兰州
Degree Name硕士
Keyword非线性发展方程 Petrov-Galerkin谱方法 KdV-Burgers方程 dual-Petrov-Galerkin谱方法
Abstract本文主要考虑了两类方程的Petrov-Galerkin谱方法:(2m+1)阶非线性发展方程和KdV-Burgers方程。对于第一类方程,我们利用Petrov-Galerkin谱方法分析了其半离散格式的稳定性和收敛性及其全离散格式的收敛性;对于第二类方程,我们利用Jie Shen提出的dual-Petrov-Galerkin谱方法给出了KdV-Burgers方程的全离散格式,并证明了其收敛性;最后给出数值例子来验证我们的理论分析。
Other AbstractWe mainly consider Petrov-Galerkin spectral method for two types of equation in this paper:(2m+1)-order nonlinear evolution equation and KdV-Burgers' equation. For the first-type equation, we use the Petrov-Galerkin spectral method to analysis the stability and convergence of its semi-discrete and the convergence of its full-discrete scheme; for the second-type equation, we use the dual-Petrov-Galerkin spectral method introduced by Jie Shen to present the full-discrete scheme of KdV-Burgers' equation, prove its convergence and give numerical examples to verify our theoretical analysis.
URL查看原文
Language中文
Document Type学位论文
Identifierhttps://ir.lzu.edu.cn/handle/262010/225368
Collection数学与统计学院
Recommended Citation
GB/T 7714
赵晓丹. 关于Petrov-Galerkin谱方法的两个问题研究[D]. 兰州. 兰州大学,2009.
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