An explicit local boundary condition is proposed for finite-domain simulations of the linear Schrödinger equation on an unbounded domain. Based on an exact boundary condition in terms of the Bessel functions, it takes a simple form with 16 neighboring grid points, and it involves no empirical parameter. While the computing load is rather low, the proposed boundary condition is effective in reflection suppression, comparable to the exact convolution treatments. An extension to nonlinear Schrödinger equations is also proposed. Numerical comparisons clearly demonstrate the effectiveness of this ALmost EXact (ALEX) boundary condition for both the linear and the cubic nonlinear Schrödinger equations.

• Received 15 September 2012

DOI:https://doi.org/10.1103/PhysRevE.86.066709