Discrete time scales with two quanta and Ulam stability

Abstract

In this study, the Ulam stability of quantum equations on time scales that alternate between two quanta is considered. We show that linear equations of first order with constant coefficient or of Euler type are Ulam stable across large regions of the complex plane, and give the best Ulam constants for those regions. We also show, however, that linear equations of first order of period-1 type are not Ulam stable for any parameter value in the complex plane. This is due to the importance of pre-positioning the non-autonomous term for Ulam stability.