Two novel linear-implicit momentum-conserving schemes for the fractional Korteweg-de Vries equation

Jingye Yan, Hong Zhang, Ziyuan Liu and Songhe Song

Applied Mathematics and Computation, 2020, vol. 367, issue C

Abstract: We propose two conservative linear-implicit schemes for the space fractional Korteweg-de Vries (fKdV) equation. One is the linear-implicit Crank–Nicolson scheme and the other is the linear-implicit leap-frog scheme. In order to obtain a high order discretization in the space direction, we adopt the Fourier pseudospectral method. The Crank–Nicolson scheme and leap-frog scheme are used for temporal discretization, and those two schemes are efficient in practical computations because of their linear property. Furthermore, we analyse the uniqueness, boundness, convergence of the two schemes. Numerical experiments are presented to validate the theoretical analysis.

Keywords: Linear-implicit Crank–Nicolson scheme; Linear-implicit leap-frog scheme; Momentum-preservation; Fourier pseudospectral method (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:367:y:2020:i:c:s0096300319307374

DOI: 10.1016/j.amc.2019.124745

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