Abstract
In this paper, we investigate some mathematical and numerical aspects of a one-dimensional nonlinear Schrodinger problem defined in a noncylindrical domain. By a change of variable, we transform the original problem into an equivalent one defined in a cylindrical domain. To obtain the existence and uniqueness of the solution, we apply the Faedo-Galerkin method and results of compactness. The numerical simulation is performed by means of the finite element method in the associated space and the finite difference method in the temporal part, to get an approximate numerical solution. In addition, we will make an analysis of the rate of convergence of the applied methods. Finally, we will show that the results of the numerical simulation are in agreement with the theoretical analysis.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
