Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: In this work  construct and analyze discrete artificial boundary conditions (ABCs) for different finite difference schemes to solve nonlinear Schrodinger equations. These new discrete boundary conditions are motivated by the continuous ABCs recently obtained by the potential strategy of Szeftel. Since these new nonlinear ABCs are based on the discrete ABCs for the linear problem  first review the ll-known results for the linear Schrodinger equation.  present our approach for a couple of finite difference schemes, including the Crank-Nicholson scheme, the Duran-Sanz-Serna scheme, the DuFort-Frankel method and several split-step (fractional-step) methods such as the Lie splitting, the Strang splitting and the relaxation scheme of Besse. Finally, several numerical tests illustrate the accuracy and stability of our new discrete approach for the considered finite difference schemes.
['Andrea Zisowsky', 'Matthias Ehrhardt']
I am writing a research paper on a idea Discrete artificial boundary conditions for nonlinear Schrödinger equations
[{"from": "human", "value": "I am writing a research paper on a idea Discrete artificial boundary conditions for nonlinear Schr\u00f6dinger equations"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: In this work  construct and analyze discrete artificial boundary conditions (ABCs) for different finite difference schemes to solve nonlinear Schrodinger equations. These new discrete boundary conditions are motivated by the continuous ABCs recently obtained by the potential strategy of Szeftel. Since these new nonlinear ABCs are based on the discrete ABCs for the linear problem  first review the ll-known results for the linear Schrodinger equation.  present our approach for a couple of finite difference schemes, including the Crank-Nicholson scheme, the Duran-Sanz-Serna scheme, the DuFort-Frankel method and several split-step (fractional-step) methods such as the Lie splitting, the Strang splitting and the relaxation scheme of Besse. Finally, several numerical tests illustrate the accuracy and stability of our new discrete approach for the considered finite difference schemes."}]