Rational spline-nonstandard finite difference scheme for the solution of time-fractional Swift–Hohenberg equation

In this paper, we introduce a new scheme based on rational spline function and nonstandard finite difference technique to solve the time-fractional Swift–Hohenberg equation in the sense of Riemann–Liouville derivative. Via Fourier method, the method is convergent and unconditionally stable. Also, we...

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Bibliographic Details
Published in:Applied mathematics and computation 2019-02, Vol.343, p.372-387
Main Authors: Zahra, W.K., Elkholy, S.M., Fahmy, M.
Format: Article
Language:English
Subjects:
Error bound
Grünwald–Letnikov derivative
Rational spline
Riemann–Liouville fractional derivative
Stability analysis
Time fractional Swift–Hohenberg equation
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Summary:In this paper, we introduce a new scheme based on rational spline function and nonstandard finite difference technique to solve the time-fractional Swift–Hohenberg equation in the sense of Riemann–Liouville derivative. Via Fourier method, the method is convergent and unconditionally stable. Also, we investigated the existence and uniqueness of the proposed method. Numerical results are demonstrated to validate the applicability and the theoretical results.
ISSN:0096-3003
1873-5649
DOI:10.1016/j.amc.2018.09.015