  The method of geodesic deviations has been applied to derive accurate
analytic approximations to geodesics in Schwarzschild space-time. The results
are used to construct analytic expressions for the source terms in the
Regge-Wheeler and Zerilli-Moncrief equations, which describe the propagation of
gravitational waves emitted by a compact massive object moving in the
Schwarzschild background space-time. The wave equations are solved numerically
to provide the asymptotic form of the wave at large distances for a series of
non-circular bound orbits with periastron distances up to the ISCO radius, and
the power emitted in gravitational waves by the extreme-mass ratio binary
system is computed. The results compare well with those of purely numerical
approaches.
