Symplectic method is applied to solve 1D time-dependent Gross-Pitaevskii(GP) equation numerically.Interference of three Bose-Einstein condensates(BECs) is investigated with or without a trapping potential.Elastic collisions of BECs occur as trapping potential exists.If trapping potential is zero at t=0,interference of three BECs is observed and oscillation of probability density is found.

With study of finite volume(FV) methods and discontinuous Galerkin(DG) method,"static reconstruction" and "dynamic reconstruction" are proposed for high-order numerical schemes.Based on the concept of "hybrid reconstruction",a new class of hybrid DG/FV schemes is presented for two-dimensional(2D) unstructured grids to solve the 2D conservation law,including 2D scalar equations and Euler equations.In the hybrid DG/FV schemes,lower-order derivatives of the piecewise polynomial are computed locally in a cell by a traditional DG method(called "dynamic reconstruction"),and the higher-order derivatives are reconstructed by the "static reconstruction" of the FV method by using lower-order derivatives in the cell and immediate neighbour cells.Typical 2D cases are given,and accuracy study is carried out.Numerical results show that the hybrid DG/FV scheme reaches desired order of accuracy.In addition,the hybrid DG/FV scheme saves great CPU time and memory compared with same order DG schemes.