  We derive fourth post-Newtonian (4PN) contributions to the Keplerian-type
parametric solution associated with the conservative dynamics of eccentric,
non-spinning compact binaries. The solution has been computed while ignoring
certain zero-average, oscillatory terms arising due to 4PN tail effects. We
provide explicit expressions for the parametric solution and various orbital
elements in terms of the conserved energy, angular momentum and symmetric mass
ratio. Canonical perturbation theory (along with the technique of Pade
approximant) is used to incorporate the 4PN nonlocal-in-time tail effects
within the action-angles framework. We then employ the resulting solution to
obtain an updated inspiral-merger-ringdown (IMR) waveform that models the
coalescence of non-spinning, moderately eccentric black hole binaries,
influenced by arXiv:1709.02007. Our updated waveform is expected to be valid
over similar parameter range as the above reference. We also present a related
waveform which makes use of only the post-Newtonian equations and thus is valid
only for the inspiral stage. This waveform is expected to work for a much
larger range of eccentricity ($e_t \lesssim 0.85$) than our full IMR waveform
(which assumes circularization of the binaries close to merger). We finally
pursue preliminary data analysis studies to probe the importance of including
the 4PN contributions to the binary dynamics while constructing gravitational
waveform templates for eccentric mergers.
