Numerical Solutions to the Time-Fractional Swift–Hohenberg Equation Using Reproducing Kernel Hilbert Space Method
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Tarih
2021
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Springer
Erişim Hakkı
info:eu-repo/semantics/closedAccess
Özet
In this work, a numerical approach based on the reproducing kernel theory is presented for solving the fractional Swift–Hohenberg equation (FS-HE) under the Caputo time-fractional derivative. Such equation is an effective model to describe a variety of phenomena in physics. The analytic and approximate solutions of FS-HE in the absence and presence of dispersive terms have been described by applying the reproducing kernel Hilbert space method (RKHSM). The benefit of the proposed method is its ability to get the approximate solution of the FS-HE easily and quickly. The current approach utilizes reproducing kernel theory, some valuable Hilbert spaces, and a normal basis. The theoretical applicability of the RKHSM is demonstrated by providing the convergence analysis. By testing some examples, we demonstrated the potentiality, validity, and effectiveness of the RKHSM. The computational results are compared with other available ones. These results indicate the superiority and accuracy of the proposed method in solving complex problems arising in widespread fields of technology and science. © 2021, The Author(s), under exclusive licence to Springer Nature India Private Limited.
Açıklama
Anahtar Kelimeler
Caputo fractional derivative, Fractional Swift–Hohenberg equation, Gram–Schmidt process, Reproducing kernel Hilbert space method
Kaynak
International Journal of Applied and Computational Mathematics
WoS Q Değeri
Scopus Q Değeri
Q2
Cilt
7
Sayı
5
