대한수학회보 (Bulletin of the Korean Mathematical Society)

  • 제57권1호
  • /
  • Pages.219-244
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  • 2020
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  • 1015-8634(pISSN)
  • /
  • 2234-3016(eISSN)
대한수학회 (Korean Mathematical Society)
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ERROR ESTIMATES FOR A GALERKIN METHOD FOR A COUPLED NONLINEAR SCHRÖDINGER EQUATIONS

  • Omrani, Khaled (Institut Superieur des Sciences Appliquees et de Technologie de Sousse Universite de Sousse) ;
  • Rahmeni, Mohamed (Ecole Superieure des Sciences et de Technologie de Hammam Sousse Universite de Sousse)
  • 투고 : 2019.02.08
  • 심사 : 2019.06.26
  • 발행 : 2020.01.31
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⟨ 이전 논문 다음 논문 ⟩

초록

In this paper, we approximate the solution of the coupled nonlinear Schrödinger equations by using a fully discrete finite element scheme based on the standard Galerkin method in space and implicit midpoint discretization in time. The proposed scheme guarantees the conservation of the total mass and the energy. First, a priori error estimates for the fully discrete Galerkin method is derived. Second, the existence of the approximated solution is proved by virtue of the Brouwer fixed point theorem. Moreover, the uniqueness of the solution is shown. Finally, convergence orders of the fully discrete Crank-Nicolson scheme are discussed. The end of the paper is devoted to some numerical experiments.

키워드

과제정보

We would like to thank the reviewers that their comments and suggestions have really improved the quality of the paper.

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