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The quasiparticle excitation spectra of a Bose gas trapped in a highlyanisotropic trap is studied with respect to varying total number of particlesby numerically solving the effective one-dimensional (1D) Gross-Pitaevskii (GP)equation proposed recently by Mateo \textit{et al.}. We obtain the staticproperties and Bogoliubov spectra of the system in the high energy domain. Thismethod is computationally efficient and highly accurate for a condensate systemundergoing a 1D to three-dimensional (3D) cigar-shaped transition, as is shownthrough a comparison our results with both those calculated by the 3D-GPequation and analytical results obtained in limiting cases. We identify theapplicable parameter space for the effective 1D-GP equation and find that thisequation fails to describe a system with large number of atoms. We alsoidentify that the description of the transition from 1D Bose-Einsteincondensate (BEC) to 3D cigar-shaped BEC using this equation is not smooth,which highlights the fact that for a finite value of $a_\perp/a_s$ the junctionbetween the 1D and 3D crossover is not perfect.

Bogoliubov excitation spectrum of an elongated condensate from quasi-one-dimensional to three-dimensional transition