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- 저자 : Mohamed Rahmeni (검색결과 2 건)
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Error estimates for a Galerkin method for a coupled nonlinear Schr\"{o}dinger equations
Khaled Omrani,Mohamed Rahmeni 대한수학회 2020 대한수학회보 Vol.57 No.1
In this paper, we approximate the solution of the coupled nonlinear Schr\"odinger 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.
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ERROR ESTIMATES FOR A GALERKIN METHOD FOR A COUPLED NONLINEAR SCHRÖDINGER EQUATIONS
Omrani, Khaled,Rahmeni, Mohamed Korean Mathematical Society 2020 대한수학회보 Vol.57 No.1
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.
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