Burgers 方程的一类不变差分格式 Alternative Title A class of invariant difference schemes for Burgers equations 朱伟 Thesis Advisor 周宇斌 2013-05-26 Degree Grantor 兰州大学 Place of Conferral 兰州 Degree Name 硕士 Keyword 李群方法 Magnus 展开 李对称 不变差分格式 Burgers 方程 Abstract 寻找保持原方程一定性质的数值格式是现代微分方程数值方法的研究热点, 李群方法和保对称的差分格式是两个重要的方向. 针对不同的偏微分方程的性 质, 构造对应的保性质的离散格式, 并用数值解去检验其效果是非常有意义的. 首先, 根据 (1+1) 维 Burgers 方程的李对称构造其不变差分格式; 同时给出关于空间离散的半离散格式. 对两种格式进行数值实验, 使用三个不同问题的数值结果检验两类方法的效果, 通过与其他方法的数值结果及精确解的比较发现,这两种方法得到了的数值结果可以较好地吻合原方程. 然后, 构造 (2+1) 维耦合的 Burgers 方程的不变差分格式; 并导出空间离散的半离散格式. 利用具体问题在不同参数下的数值结果检验方法的有效性, 并对本文的数值结果与其他的结果进行了对比分析. Other Abstract To preserve the physical properties of the original equation is the research focus of modern numerical analysis, Lie group method and invariant difference scheme are two important fields. Constructing the discrete schemes according to PDEs’ properties and testing the numerical results are very meaningful. First, construct Burgers equation’s invariant difference scheme according to the the (1+1) dimensional Burgers equation’s symmetry; and construct a semi- discrete schemes based on discreted space. Three test problems have been studied to demonstrate the accuracy of the present two methods. The results, which have copared with the exact solution and other numerical method’s results, are found to be in better agreement with exact solution. Second, invariant difference schemes and semi-discrete schemes are obtained according to (2+1) dimensional coupled Burgers equation’s properties. Initial boundary value problems are used to test the accuracy of the two methods. URL 查看原文 Language 中文 Document Type 学位论文 Identifier https://ir.lzu.edu.cn/handle/262010/225733 Collection 数学与统计学院 Recommended CitationGB/T 7714 朱伟. Burgers 方程的一类不变差分格式[D]. 兰州. 兰州大学,2013.
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