Family of finite-difference schemes with transparent boundary conditions for the nonstationary Schr?dinger equation in a semi-infinite strip

摘要

A study was conducted to demonstrate a range of finite-difference schemes with transparent boundary conditions for the nonstationary Schr?dinger equation in a semi-infinite strip. The initial-boundary value problem for the generalized Schr?dinger equation was solved in a semi-infinite strip. A new range of two-level finite-difference schemes with averaging over spatial variables on a finite grid was constructed to solve the problem. The two-level finite-difference schemes covered a set of finite-difference schemes constructed by various methods. It was demonstrated that the range of two-level finite-difference schemes was absolutely stable in two norms with respect to both initial data and free terms when considered with an abstract transparent boundary condition (TBC).