http://chineseinput.net/에서 pinyin(병음)방식으로 중국어를 변환할 수 있습니다.
변환된 중국어를 복사하여 사용하시면 됩니다.
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.
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.
A fourth-order accurate finite difference scheme for the extended-Fisher-Kolmogorov equation
Tlili Kadri,Khaled Omrani 대한수학회 2018 대한수학회보 Vol.55 No.1
In this paper, a nonlinear high-order difference scheme is proposed to solve the Extended-Fisher-Kolmogorov equation. The existence, uniqueness of difference solution and priori estimates are obtained. Furthermore, the convergence of the difference scheme is proved by utilizing the energy method to be of fourth-order in space and second-order in time in the discrete $L^{\infty}$-norm. Some numerical examples are given in order to validate the theoretical results.
A FOURTH-ORDER ACCURATE FINITE DIFFERENCE SCHEME FOR THE EXTENDED-FISHER-KOLMOGOROV EQUATION
Kadri, Tlili,Omrani, Khaled Korean Mathematical Society 2018 대한수학회보 Vol.55 No.1
In this paper, a nonlinear high-order difference scheme is proposed to solve the Extended-Fisher-Kolmogorov equation. The existence, uniqueness of difference solution and priori estimates are obtained. Furthermore, the convergence of the difference scheme is proved by utilizing the energy method to be of fourth-order in space and second-order in time in the discrete $L^{\infty}-norm$. Some numerical examples are given in order to validate the theoretical results.