CONSTRUCTION OF ASYMPTOTIC SOLUTIONS TO DISCRETE BESSEL EQUATIONS

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.