  Individual supermassive black hole binaries in non-circular orbits are
possible nanohertz gravitational wave sources for the rapidly maturing Pulsar
Timing Array experiments. We develop an accurate and efficient approach to
compute Pulsar Timing Array signals due to gravitational waves from inspiraling
supermassive black hole binaries in relativistic eccentric orbits. Our approach
employs a Keplerian-type parametric solution to model third post-Newtonian
accurate precessing eccentric orbits while a novel semi-analytic prescription
is provided to model the effects of quadrupolar order gravitational wave
emission. These inputs lead to a semi-analytic prescription to model such
signals, induced by non-spinning black hole binaries inspiralling along
arbitrary eccentricity orbits. Additionally, we provide a fully analytic
prescription to model Pulsar Timing Array signals from black hole binaries
inspiraling along moderately eccentric orbits, influenced by Boetzelet
al.[Phys. Rev. D 96,044011(2017)]. These approaches are being incorporated into
Enterprise and TEMPO2 for searching the presence of such binaries in Pulsar
Timing Array datasets.
