Instruments and Systems: Monitoring, Control, and Diagnostics Annotation << Back An Algorithm for Constructing Approximate Solutions to the Equations of Mathematical Models of a Simulator of Human Respiration and Metabolism YU.YU. GROMOV, V.A. POGONIN, N.V. GOMZOV, K.A. SLEZIN The article proposes an algorithm for constructing approximate solutions to the equations of mathematical models of a simulator of respiration and metabolism. The Artificial Lungs – Insulating Breathing Apparatus (IL–IDA) system is presented, designed to analyze and predict the operation of insulating breathing apparatus in an inhospitable atmosphere. The model considers key processes: gas exchange, CO2 sorption, heat transfer and hydrodynamics of gas fl ows. To simplify the model, several physical sound assumptions are introduced, such as ideal mixing of gases, isothermal processes and laminar fl ow regime. The system is decomposed into interconnected subsystems formalized using ordinary differential equations and algebraic relations. The algorithm includes blocks for preparing the previously proposed mathematical models for direct use of the methods of approximate analysis proposed in the work. The proposed methods are based on the use of continued fractions, which makes it possible to achieve a reasonable compromise between the number of calculations involved and the accuracy of the approximate solutions obtained. This is of particular importance since it is necessary to repeatedly build an approximate solution to the equations of a mathematical model when solving problems of parametric identifi cation and control. The algorithm for constructing approximate solutions is tested in the work on a test example with an analytical solution. Graphs and tables are constructed, the analysis of which allows us to conclude that the proposed algorithm is working and that it is appropriate to use it to construct approximate solutions to the equations of the mathematical model. Keywords: approximate solution algorithm, insulation breathing apparatus, artificial lungs, gas exchange, regenerative cartridge, mathematical model. DOI: 10.25791/pribor.1.2026.1643 Pp. 18-31.