摘要

In this study, we reveal an approximate linear relation for Bessel functions of the first kind, based on asymptotic analyses. A set of coefficients are calculated from a linear algebraic system. For any given error tolerance, a Bessel function of an order big enough is approximated by a linear combination of those with neighboring orders using these coefficients. This naturally leads to a class of ALmost EXact (ALEX) boundary conditions in atomic and multiscale simulations.