分数阶偏微分方程的小波自适应求解

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 Title	Wavelet 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 Abstract	In 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
Identifier	https://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.

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