Abstract: An improved shooting method is applied to 1D Gross-Pitaevskii equation,which describes Bose-Einstein condensate of neutral atoms in harmonic trapping potential at zero temperature.Eigenvalues of ground state of condensates with different nonlinear coefficient are given.Interference of three condensates after removing the trapping potential is studied with symplectie method.A periodic evolution is shown.Influence of relative phase on interference of condensates is discussed.

Key words: shooting method, Gross-Pitaevskii equation, interference