|本期目录/Table of Contents|

[1]朱莉.分数阶偏微分方程的小波算子矩阵解法[J].厦门理工学院学报,2017,(3):75-82.
 ZHU Li.Solving Fractional Partial Differential Equations byUsing the Wavelet Operational Matrix Method[J].Journal of JOURNAL OF XIAMEN,2017,(3):75-82.
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分数阶偏微分方程的小波算子矩阵解法(PDF)
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《厦门理工学院学报》[ISSN:1673-4432/CN:35-1289/Z]

卷:
期数:
2017年第3期
页码:
75-82
栏目:
应用数理科学
出版日期:
2017-06-30

文章信息/Info

Title:
Solving Fractional Partial Differential Equations by Using the Wavelet Operational Matrix Method
文章编号:
1673-4432(2017)03-0075-08
作者:
朱莉
(厦门理工学院应用数学学院,福建 厦门 361024)
Author(s):
ZHU Li
(School of Applied Mathematics,Xiamen University of Technology,Xiamen 361024,China)
关键词:
分数阶偏微分方程算子矩阵第二类Chebyshev小波Sylvester方程
Keywords:
fractional partial differential equationsoperational matrixsecond Chebyshev waveletSylvester equation
分类号:
O2418
DOI:
-
文献标志码:
A
摘要:
推导并利用第二类Chebyshev小波的分数阶积分算子矩阵,给出了求解一类分数阶偏方程的数值方法,并证明了二元函数第二类Chebyshev小波展式的收敛性。研究结果表明,基于第二类Chebyshev小波算子矩阵的方法可将分数阶阶偏微分方程转化成Sylvester方程求解,减少方程的计算量。数值算例表明,随着参数m’的增大,数值解与精确解可以很好地吻合,证明了基于第二类Chebyshev小波算子矩阵方法数值求解分数阶偏微分方程的有效性和精确性。
Abstract:
In this paper,the second Chebyshev wavelet operational matrix of fractional integration is derived and used to solve a kind of fractional differential equations.Then the convergence of the twodimensional second Chebyshev wavelet is proved.The initial equations are transformed into a Sylvester equation based on the proposed the second Chebyshev wavelet operational matrix method,which reduced the calculation time.Numerical examples are included to demonstrate that the numerical solutions are in very good agreement with exact solution when the value of m′ is increasing.Therefore,the proposed second Chebyshev wavelet operational matrix method is accurate and effective.

参考文献/References:

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相似文献/References:

[1]朱莉.非线性分数阶Volterra积分微分方程的SCW数值方法[J].厦门理工学院学报,2015,(3):96.[doi:10.3969/j.issn.1673-4432.2015.03.018]
 ZHU Li.Numerical Solution of Nonlinear FractionalOrder Volterra IntegroDiferential Equations by SCW[J].Journal of JOURNAL OF XIAMEN,2015,(3):96.[doi:10.3969/j.issn.1673-4432.2015.03.018]

备注/Memo

备注/Memo:
[收稿日期]2017-04-10[修回日期]2017-06-15 [作者简介]朱莉(1984-),女,副教授,博士,研究方向为微分方程数值解,Email:zhulwhu@163.com。
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