AbstractThis work is a study of approximate methods for the solution of problems in space-dependent nuclear reactor dynamics. It is shown that these approximate methods can all be considered applications of the method of weighted residuals. In each method, a trial solution is formed for the neutron flux by making expansions in known spatially dependent functions called trial functions. Each approximate method differs from the others in the manner in which its trial functions are chosen. The undetermined time-dependent functions, called amplitude functions, are then found by using the weighted-residual procedure known as the method of undetermined functions to derive the so-called multimode kinetics equations, which are first-order ordinary differential equations in time. The multimode kinetics equations are then integrated using the method of undetermined parameters. Weighted-residual procedures are thus used for both spatial and temporal integrations. Some numerical results are reported for continuous synthesis and multichannel systhesis approximations. Several choices of weighting functions are compared. Conclusions are drawn regarding the roles of the trial functions and the weighting functions in obtaining accurate solutions.