关于Petrov-Galerkin谱方法的两个问题研究

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 Title	Research 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 Abstract	We 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
Identifier	https://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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