Analysis of High-Order Absorbing Boundary Conditions for the Schrödinger Equation (Communications in Computational Physics, 2011)
The paper is concerned with the numerical solution of Schrödinger equationson an unbounded spatial domain. High-order absorbing boundary conditionsfor one-dimensional domain are derived, and the stability of the reduced initial boundaryvalue problem in the computational interval is proved by energy estimate. Then asecond order finite difference scheme is proposed, and the convergence of the schemeis established as well. Finally, numerical examples are reported to confirm our errorestimates of the numerical methods.