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Post-Newtonian expansions of the binding energy and gravitational wave fluxtruncated at the {\it same relative} post-Newtonian order form the basis of the{\it standard adiabatic} approximation to the phasing of gravitational wavesfrom inspiralling compact binaries. Viewed in terms of the dynamics of thebinary, the standard approximation is equivalent to neglecting certainconservative post-Newtonian terms in the acceleration. In an earlier work, wehad proposed a new {\it complete adiabatic} approximant constructed from theenergy and flux functions. At the leading order it employs the 2PN energyfunction rather than the 0PN one in the standard approximation, so that,effectively the approximation corresponds to the dynamics where there are nomissing post-Newtonian terms in the acceleration. In this paper, we compare theoverlaps of the standard and complete adiabatic templates with the exactwaveform in the adiabatic approximation of a test-mass motion in theSchwarzschild spacetime, for the VIRGO and the Advanced LIGO noise spectra. Itis found that the complete adiabatic approximants lead to a remarkableimprovement in the {\it effectualness} at lower PN ($<$ 3PN) orders, whilestandard approximants of order $\geq$ 3PN provide a good lower-bound to thecomplete approximants for the construction of effectual templates. {\itFaithfulness} of complete approximants is better than that of standardapproximants except for a few post-Newtonian orders. Standard and completeapproximants beyond the adiabatic approximation are also studied using theLagrangian templates of Buonanno, Chen and Vallisneri.Comment: Proceedings of the GWDAW-9, Accepted for publication in Class. Quant.  Gra

Complete adiabatic waveform templates for a test mass in the Schwarzschild spacetime: VIRGO and advanced LIGO studies