Mixed analytic-numerical solutions for a simple radiating system

A procedure is presented for dealing with fast radiating systems. It employs a method of matching a numerical solution in the source region to an analytic solution in the outer region. As a test of its effectiveness it is applied to a simple radiating system composed of a nonrelativistic harmonic oscillator coupled to a spherically symmetric scalar field. The effects of radiation damping on the oscillator are readily calculated and agree with the exact analytic predictions that one can derive. The accuracy of the monopole formula is checked and shown to fail in the fast-motion regime. It is also shown that the asymptotic damping of the system is independent of the initial conditions as long as the total energy is positive and constant. An instability of the system is also discussed.Work supported in part by NSF Grant No. PHY-8503879.