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

W.K. Zahra, S.M. Elkholy and M. Fahmy

Applied Mathematics and Computation, 2019, vol. 343, issue C, 372-387

Abstract: 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.

Keywords: Rational spline; Riemann–Liouville fractional derivative; Grünwald–Letnikov derivative; Time fractional Swift–Hohenberg equation; Stability analysis; Error bound (search for similar items in EconPapers)
Date: 2019
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:343:y:2019:i:c:p:372-387

DOI: 10.1016/j.amc.2018.09.015

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