We construct four finite-difference models for the Bessel differential
equation. They correspond respectively, to the standard, Numerov, Mic
kens-Bamadhani, and combined Numerov-Mickens schemes. The asymptotic b
ehavior of the solutions to these difference equations is calculated a
nd compared to the asymptotic solution of the Bessel differential equa
tion. These results are then related to the problem of numerically int
egrating Schrodinger type ordinary differential equations.