Abstract
The time-dependent Schrodinger equation is the key one in many fields. It should be often solved in unbounded space domains. Several approaches are known to deal with such problems using approximate transparent boundary conditions (TBCs) on the artificial boundaries. Among them, there exist the so-called discrete TBCs whose advantages are the complete absence of spurious reflections, reliable computational stability, clear mathematical background and the corresponding rigorous stability theory. In this paper, the Strang-type splitting with respect to the potential is applied to three two-level schemes with different discretizations in space having the approximation order O(τ 2 + | h | k ), k = 2 or 4. Explicit forms of the discrete TBCs are given and results on existence, uniqueness and uniform in time L 2-stability of solutions are stated in a unified manner. Due to splitting, an effective direct algorithm to implement the schemes is presented for general potential.
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.
