An implicit semi-linear discretization of a bi-fractional Klein-Gordon-Zakharov system which conserves the total energy
type: Item
instance of: scholarly article
title: An implicit semi-linear discretization of a bi-fractional Klein-Gordon-Zakharov system which conserves the total energy
zbMATH Open document ID: 1475.35321
author: Romeo Martínez
author: Jorge Eduardo Macías-Díaz
author: Qin Sheng
published in: Applied Numerical Mathematics
publication date: 2021-08-05T00:00:00Z
Mathematics Subject Classification ID: 35Q55
Mathematics Subject Classification ID: 35A01
Mathematics Subject Classification ID: 35A02
Mathematics Subject Classification ID: 65M06
Mathematics Subject Classification ID: 65M12
Mathematics Subject Classification ID: 65N06
Mathematics Subject Classification ID: 26A33
Mathematics Subject Classification ID: 35R11
zbMATH DE Number: 7379325
zbMATH Keywords: fractional-order Klein-Gordon-Zakharov equations
zbMATH Keywords: conservation of energy
zbMATH Keywords: Riesz space-fractional equations
zbMATH Keywords: energy-conserving method
zbMATH Keywords: fractional-order centered differences
zbMATH Keywords: numerical efficiency analysis
MaRDI profile type: Publication
full work available at URL: j.apnum.2021.06.014
OpenAlex ID: W3180263986
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cites work: A Theoretical Basis for the Application of Fractional Calculus to Viscoelasticity
cites work: Numerical solution of the sine-Gordon equation
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cites work: Optimal existence and uniqueness theory for the fractional heat equation
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cites work: Fourth-order methods for space fractional reaction–diffusion equations with non-smooth data
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DOI: 10.1016/J.APNUM.2021.06.014