We have constructed an integrated method to model the system of measuring the density of flows of infrared radiation based on solving the inverse problems of dynamics using the Volterra equation of the first kind and focusing on solving the problem on dynamic correction. Solving a problem on the structural correction of the dynamic characteristics of the system for measuring the density of flows implies the construction and application in a transforming channel or a circuit in the system of a certain unit. This unit, owing to its specially formed dynamic properties, ensures the best dynamic characteristics of the entire system. We have experimentally verified the technique for the compensation for a dynamic error. To this end, the experiments were conducted to measure the density of a non-stationary flow of infra-red radiation with the assigned law of change, which is characteristic of the practical working conditions for receivers. A change in the density of the incident flow of infrared radiation was achieved at the expense of the receiver's rotation around the axis that passes through the middle of its receiving surface, in the flow of the stationary emitter. The result of the experiment is the derived nonlinear approximation of the experimentally obtained transitional characteristic in the form of the receiver's response to the sinusoidal flow of infrared radiation. It should be specifically noted that the results of numerical simulation and the experiment show a satisfactory convergence, which allows us to argue about the correct choice of the model. The developed algorithms are capable to provide a numerical implementation of integrated models and serve as the basis for constructing high-performance specialized microprocessor systems to work in real time. That has made it possible to successfully implement the dynamic correction of the system for measuring flows of infrared radiation and to significantly increase its accuracy. A combined application of the devised method for solving mathematical problems and computer tools would provide an opportunity to improve the efficiency of processes to synthesize and design computational devices for correcting means of measurement