The earlier proposed algorithm for numerical solution of the quasi-optical equation for the transversal correlation function of radiation field applicable to studying dynamics of amplified spontaneous radiation (ASR) in X laser is being improved. The numerical method is based on discretization of the transversal differential operator and obtaining a system of connected differential equations of the first order in the longitudinal variable which is solved with an explicit method. A multi-stage explicit integration scheme is used, procedures are introduced for phase error reduction and solution smoothing. A good accuracy of the method and possibility to solve ASR dynamics problems under characteristic conditions are shown by numerical examples.