A method for guiding a multistage interceptor missile toward a target missile that may transition from a boost mode to a ballistic mode during the engagement. The method comprises the steps of tracking the position of the target missile with a sensor, generating a predicted intercept point and time, and loading the predicted intercept point and time into the interceptor missile guidance system. The interceptor missile is launched and transition is made to the second stage of propulsion of the interceptor missile. Second-stage midcourse guidance acceleration commands are generated in response to an elevated predicted intercept point generated using the Runge-Kutta integration method working on predicted target missile position, velocity, and acceleration. During third stage propulsion said interceptor missile is guided toward an updated predicted intercept point of the target missile. During fourth stage, the kinetic warhead effects a hit-to-kill intercept of the target missile.