Point kinetic equations (PKEs) represent a simplified approach to study the reactor transients at first hand, and help to develop an insight for reactor control, operation and safety. Several methods have been around for over last five decades for accurate, stable, and reliable solution of PKEs however, their realization has become possible with the advent of modern computers. Additionally, the stiffness of PKEs inspires researchers to seek further for more robust algorithms. In this paper, an explicit algorithm based upon Generating Function Method (GFM) is proposed for the solution of such a complex system of differential equations. The method was implemented to solve conventional reactivity problems, such as step, ramp, and sinusoidal reactivity insertions and compared with the other numerical algorithms. In these problems, GFM has been found to provide numerical estimates of neutron population with comparable accuracy to other algorithms, and it is computationally efficient and relatively stable. In order to explore the feasibility of the GFM for problems in reactor dynamics, a delayed-supercritical process with temperature feedback was also simulated, and results found were numerically equivalent to available techniques, however with lesser computational effort and time.