The paper deals with the comparison between the frequency domain and time domain analysis of transient electric field generated by the ground penetrating radar (GPR) dipole antenna and transmitted into the dielectric half-space for GPR antenna. The time domain integral equation (TDIE) approach is based on the Hallen integral equation for half-space problems. The numerical solution is carried out via the space-time scheme of the Galerkin-Bubnov Indirect Boundary Element Method (GB-IBEM). The frequency domain formulation is based on the Pocklington’s integro-differential equation which is solved by using the frequency domain scheme of the Galerkin Bubnov Indirect Boundary Element Method. The related transient response is obtained by means of the Inverse Fast Fourier Transform (IFFT). The Integral Equation combined with the transmission coefficient arising from modified image theory (MIT) represents the novel method for obtaining the transmitted electric field of a GPR antenna. This paper brings the comparison of the results obtained by different approaches in solving the Integral Equation. The calculated results agree satisfactorily.