The use of a hybrid computer results in an efficient method of analyzing the transience in high-performance nuclear reactor cores using ceramic fuels such as UO2. The nature of the space dependence of the variables is such that a great deal of multiplexing of computer components is possible. Asa consequence of multiplexing, an iterative procedure is necessary to obtain the closed-loop system response for a finite (but arbitrary) interval of time. A mathematical proof of the uniform convergence of the iterative process has been obtained. This proof is based on the principle of contraction mapping. The economy which may be realized in computer equipment and programming effort for this area of system analysis is discussed with illustrative examples. The computing techniques developed are applicable to the analysis of any nonlinear feedback control system.