The construction of higher-order numerical approximation formula for Riesz derivative and its application to nonlinear fractional differential equations (I)

The main goal of this paper is to construct high-order numerical differential formulas approximating the Riesz derivative and apply them to the numerical solution of the nonlinear space fractional Ginzburg–Landau equations. Firstly, we introduce a novel second-order fractional central difference ope...

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Bibliographic Details
Published in:	Communications in nonlinear science & numerical simulation Vol. 110; p. 106394
Main Authors:	Ding, Hengfei, Yi, Qian
Format:	Journal Article
Language:	English
Published:	Amsterdam Elsevier B.V 01.07.2022 Elsevier Science Ltd
Subjects:	Approximation Convergence Differential equations Energy methods Finite difference method Finite differences Fractional calculus Fractional-compact numerical algorithm Fractions Landau-Ginzburg equations Mathematical analysis Nonlinear space fractional Ginzburg–Landau equations Norms Operators (mathematics) Riesz derivative Stability Riesz derivative Fractional-compact numerical algorithm Stability Nonlinear space fractional Ginzburg–Landau equations Convergence
ISSN:	1007-5704, 1878-7274
Online Access:	Get full text
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