Abstract: A model equation shows that the conventional method gives very wr ong results for the time step just basedon the advection part, if the time scale of the source term is much smaller than that of the advection par t. Even ift he sour ce term is a small quantity compared with the advection par t, the large scale structure is completely wrong.In or der to over come the numerical difficulty, consider the operator splittingmethod. After splitting, the mean flowpart ( advection part) will be treated using any suitable numerical method, while the sour ce step ( ODE) is solvedanalytically. With such a met hod, one can use a time step just based on the t ime scale of the advection par t to cap2ture the cor rect large scale, independently of how small the time scale of the sour ce term is. This method is appliedto t he Euler equations with an oscillation source term. The satisfying results are given.

Key words: source terms, stiffness problem, mixed analytical/n umerical scheme