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A new numerical method of calculating the Hartree-Fock-Bogoliubov (HFB) and time-dependent HFB (TDHFB) with the Gogny interaction is proposed. The three-dimensional harmonic-oscillator (3DHO) basis functions are replaced by one-dimensional spatial grid points of Lagrange mesh plus two-dimensional harmonic-oscillator basis functions in the perpendicular plane to the direction of the spatial grid points [Lagrange mesh and harmonic oscillator (LMHO)]. By using the LMHO, the calculations of the HFB and TDHFB are carried out in the typical nuclei of 20O and 34Mg as an illustration of the feasibility of the TDHFB formulation with the LMHO. The strength functions of the quadrupole vibrations (K=0) are obtained and are compared with the ones calculated with the 3DHO

Time-dependent Hartree-Fock-Bogoliubov calculations using a Lagrange mesh with the Gogny interaction