Abstract
This paper is concerned with the time-step condition (or grid ratio condition) of finite difference method for solving the Gross–Pitaevskii equation with an angular momentum rotation term. An optimal error estimate of the finite difference method in H1 norm is established without any constraints of the grid ratios. Besides the standard energy method, a ‘cut-off’ function technique and a ‘lifting’ technique is introduced in analyzing the proposed scheme. The analysis method used in this paper can be applied to many other finite difference schemes for solving the nonlinear Schrödinger-type equations for which previous works often require certain restriction on the grid ratios. Numerical results are reported to verify the error estimates and conservation laws.
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.
