The construction of higher-order numerical approximation formula for Riesz derivative and its application to nonlinear fractional differential equations (I)-Reference-Cited by-同舟云学术

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

Published:2022-07 Issue: Volume:110 Page:106394
ISSN:1007-5704
Container-title:Communications in Nonlinear Science and Numerical Simulation
language:en
Short-container-title:Communications in Nonlinear Science and Numerical Simulation

Author:

Ding Hengfei,Yi Qian^ORCID

Publisher

Elsevier BV

Subject

Applied Mathematics,Modeling and Simulation,Numerical Analysis

Reference50 articles.

1. An implicit midpoint difference scheme for the fractional Ginzburg–Landau equation;Wang;J Comput Phys,2016

2. An unconditionally stable linearized difference scheme for the fractional Ginzburg–Landau equation;He;Numer. Algorithms,2018

3. Fractional quantum mechanics;Laskin;Phys. Rev. E.,2000

4. Crank-nicolson difference scheme for the coupled nonlinear Schrödinger equations with the Riesz space fractional derivative;Wang;J Comput Phys,2013

5. Numerical methods for fractional partial differential equations with Riesz space fractional derivatives;Yang;Appl Math Model,2010

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