兰州大学机构库 >数学与统计学院
分数阶偏微分方程的小波自适应求解
Alternative TitleWavelet Adaptive Method for Solving Fractional Partial Differential Equations
张治江
Thesis Advisor邓伟华
2014-05-29
Degree Grantor兰州大学
Place of Conferral兰州
Degree Name硕士
Keyword分数阶偏微分方程 小波自适应 快速小波变换 小波压缩
Abstract本文主要考虑了小波自适应方法在求解分数阶偏微分方程中的应用。分数阶算子的非局部化特征使得分数阶微分方程的求解需要很大的计算量,此时对于一类含有局部结构的问题自适应方法较一致性方法具有更大的优势。 我们利用小波的压缩性,把小波逼近系数的量级作为一个指示子去设计自适应算法,动态的调整逼近基底中小波的位置和数目,在保证计算精度的同时显著的降低了计算花费。这些算法简单易行,数值算例验证了它们的有效性。
Other AbstractIn this paper, we consider the wavelet adaptive methods for solving fractional partialvdifferential equations. Due to the non-Locality characteristic of fractional operators, the solutions for the fractional differential equations require a large amount of computation. For a class of problems which containing the local structure, the adaptive approach compared with the uniform method tends to a great of advantage. We use the magnitude of the wavelet approximation coefficients to design an adaptive algorithm, which dynamically adjust the location and number of basis functions, ensuring the accuracy and significantly reducing the computational cost. These algorithms are simple, some numerical examples are given to verify their validity.
URL查看原文
Language中文
Document Type学位论文
Identifierhttps://ir.lzu.edu.cn/handle/262010/225422
Collection数学与统计学院
Recommended Citation
GB/T 7714
张治江. 分数阶偏微分方程的小波自适应求解[D]. 兰州. 兰州大学,2014.
Files in This Item:
There are no files associated with this item.
Related Services
Recommend this item
Bookmark
Usage statistics
Export to Endnote
Altmetrics Score
Google Scholar
Similar articles in Google Scholar
[张治江]'s Articles
Baidu academic
Similar articles in Baidu academic
[张治江]'s Articles
Bing Scholar
Similar articles in Bing Scholar
[张治江]'s Articles
Terms of Use
No data!
Social Bookmark/Share
No comment.
Items in the repository are protected by copyright, with all rights reserved, unless otherwise indicated.