The advent of asynchronous iterative scheme gives high efficiency to numerical computations. However, it is generally difficult to handle the problems of resource management and convergence detection. This paper uses JACK2, an asynchronous communication kernel library for iterative algorithms, to implement both classical and asynchronous parareal algorithms, especially the latter. We illustrate the measures whereby one can tackle the problems above elegantly for the time-dependent case. Finally, experiments are presented to prove the availability and efficiency of such application.