Point-Symmetric Extension-Based Interval Shannon-Cosine Spectral Method for Fractional PDEs

Ruyi Xing, Yanqiao Li, Qing Wang, Yangyang Wu and Shu-Li Mei

Discrete Dynamics in Nature and Society, 2020, vol. 2020, 1-10

Abstract:

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.

Date: 2020
References: Add references at CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://downloads.hindawi.com/journals/DDNS/2020/4565036.pdf (application/pdf)
http://downloads.hindawi.com/journals/DDNS/2020/4565036.xml (text/xml)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hin:jnddns:4565036

DOI: 10.1155/2020/4565036

Access Statistics for this article

More articles in Discrete Dynamics in Nature and Society from Hindawi
Bibliographic data for series maintained by Mohamed Abdelhakeem ().