September 01, 2018

Galerkin-Legendre spectral schemes for nonlinear space fractional Schrödinger equation

  • Fan W.
  • Jiang X.
  • Wang C.
  • Zhang H.

© 2017, Springer Science+Business Media, LLC, part of Springer Nature. In the paper, we first propose a Crank-Nicolson Galerkin-Legendre (CN-GL) spectral scheme for the one-dimensional nonlinear space fractional Schrödinger equation. Convergence with spectral accuracy is proved for the spectral approximation. Further, a Crank-Nicolson ADI Galerkin-Legendre spectral method for the two-dimensional nonlinear space fractional Schrödinger equation is developed. The proposed schemes are shown to be efficient with second-order accuracy in time and spectral accuracy in space which are higher than some recently studied methods. Moreover, some numerical results are demonstrated to justify the theoretical analysis.

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© 2017 International World Wide Web Conference Committee (IW3C2), published under Creative Commons CC BY 4.0 License. Many of today's websites have recognised the importance of mobile friendly pages to keep users engaged and to provide a satisfying user experience. However, next to the experience provided by the sites themselves, ...

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© 2017 International World Wide Web Conference Committee (IW3C2), published under Creative Commons CC BY 4.0 License. Uber is a popular ride-sharing application that matches people who need a ride (or riders) with drivers who are willing to provide it using their personal vehicles. Despite its growing popularity, there exist ...

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© 2017 International World Wide Web Conference Committee (IW3C2), published under Creative Commons CC BY 4.0 License. Recent studies in social media spam and automation provide anecdotal argumentation of the rise of a new generation of spambots, so-called social spambots. Here, for the first time, we extensively study this novel ...