Fully discrete spectral methods for solving time fractional nonlinear Sine–Gordon equation with smooth and non-smooth solutions

Zeting Liu, Shujuan Lü and Fawang Liu

Applied Mathematics and Computation, 2018, vol. 333, issue C, 213-224

Abstract: We consider the initial boundary value problem of the time fractional nonlinear Sine–Gordon equation and the fractional derivative is described in Caputo sense with the order α(1 < α < 2). Two fully discrete schemes are developed based on Legendre spectral approximation in space and finite difference discretization in time for smooth solutions and non-smooth solutions, respectively. Numerical stability and convergence are analysed. Numerical experiments for both the fully discrete schemes are presented to confirm our theoretical analysis.

Keywords: Time fractional nonlinear Sine–Gordon equation; Legendre spectral method; Stability and convergence; Caputo derivative; Smooth and non-smooth solutions (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:333:y:2018:i:c:p:213-224

DOI: 10.1016/j.amc.2018.03.069

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