An efficient numerical method for simulating the dynamics of coupling Bose–Einstein condensates in optical resonators

In this paper, we present an efficient numerical method for computing the dynamics of coupling Bose–Einstein condensates in optical resonators at extremely low temperature, which is modeled by Gross–Pitaevskii equations (GPEs) coupled with an integral and ordinary differential equation (IODE). Our numerical method is based on an integration factor method for solving the IODE and a time-splitting sine pseudospectral method for solving the GPEs. Our numerical method keeps well the dynamical properties of the mathematical model and have spectral accuracy in space. Through extensive numerical simulations, we analyze which factors may be useful for uniting Bose–Einstein condensates in optical resonators and study the possible way of dynamically uniting two Bose–Einstein condensates in optical resonators.