The paper is concerned with the numerical solution of Schr ̈odinger equations on an unbounded spatial domain. High-order absorbing boundary conditions for one-dimensional domain are derived, and the stability of the reduced initial boundary value problem in the computational interval is proved by energy estimate. Then a second order finite difference scheme is proposed, and the convergence of the scheme is established as well. Finally, numerical examples are reported to confirm our error estimates of the numerical methods.
Scopus Subject Areas
- Physics and Astronomy (miscellaneous)
- Finite differencemethod
- High-order absorbing boundary condition
- Schrodinger equation