Point-Symmetric Extension-Based Interval Shannon-Cosine Spectral Method for Fractional PDEs
Joint Authors
Mei, Shu-Li
Ruyi, Xing
Li, Yanqiao
Wang, Qing
Wu, Yangyang
Source
Discrete Dynamics in Nature and Society
Issue
Vol. 2020, Issue 2020 (31 Dec. 2020), pp.1-10, 10 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2020-06-02
Country of Publication
Egypt
No. of Pages
10
Main Subjects
Abstract EN
The approximation accuracy of the wavelet spectral method for the fractional PDEs is sensitive to the order of the fractional derivative and the boundary condition of the PDEs.
In order to overcome the shortcoming, an interval Shannon-Cosine wavelet based on the point-symmetric extension is constructed, and the corresponding spectral method on the fractional PDEs is proposed.
In the research, a power function of cosine function is introduced to modulate Shannon function, which takes full advantage of the waveform of the Shannon function to ensure that many excellent properties can be satisfied such as the partition of unity, smoothness, and compact support.
And the interpolative property of Shannon wavelet is held at the same time.
Then, based on the point-symmetric extension and the general variational theory, an interval Shannon-Cosine wavelet is constructed.
It is proved that the first derivative of the approximated function with this interval wavelet function is continuous.
At last, the wavelet spectral method for the fractional PDEs is given by means of the interval Shannon-Cosine wavelet.
By means of it, the condition number of the discrete matrix can be suppressed effectively.
Compared with Shannon and Shannon-Gabor wavelet quasi-spectral methods, the novel scheme has stronger applicability to the shockwave appeared in the solution besides the higher numerical accuracy and efficiency.
American Psychological Association (APA)
Ruyi, Xing& Li, Yanqiao& Wang, Qing& Wu, Yangyang& Mei, Shu-Li. 2020. Point-Symmetric Extension-Based Interval Shannon-Cosine Spectral Method for Fractional PDEs. Discrete Dynamics in Nature and Society،Vol. 2020, no. 2020, pp.1-10.
https://search.emarefa.net/detail/BIM-1153062
Modern Language Association (MLA)
Ruyi, Xing…[et al.]. Point-Symmetric Extension-Based Interval Shannon-Cosine Spectral Method for Fractional PDEs. Discrete Dynamics in Nature and Society No. 2020 (2020), pp.1-10.
https://search.emarefa.net/detail/BIM-1153062
American Medical Association (AMA)
Ruyi, Xing& Li, Yanqiao& Wang, Qing& Wu, Yangyang& Mei, Shu-Li. Point-Symmetric Extension-Based Interval Shannon-Cosine Spectral Method for Fractional PDEs. Discrete Dynamics in Nature and Society. 2020. Vol. 2020, no. 2020, pp.1-10.
https://search.emarefa.net/detail/BIM-1153062
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1153062