In connection with the fact that the heat capacity of air and checker are complex temperature functions, these differential equations cannot be solved analytically; their solution is further complicated by the presence of coils and atmospheric humidity. The differential equations of nonstationary heat exchange in regenerators can be solved when these equations are integrated numerically, written in terms of finite differences for the checker height and the blast time as parameters. Numerical integration is only possible when a digital computer is available. For this purpose the regenerator length (checker height) must be divided into n equal sections. For each time interval the temperature variations of the gas passing gradually through the individual checker sections, and the checker temperature variations in each section in the time intervals considered are calculated from the equations of heat transfer and heat balance. The calculation is carried out until air (heat) blast is stopped; then begins an analog calculation of the period of cold blast by the products of fractionation carried out from the last section to the first. When these calculations are made for a regenerator with what is called triple blast, the cold-blast calculations must be followed by similar ones for the period of loop blast. After the end of cold blast and loop blast, air blast sets in again which is again followed by cold blast and loop blast and so on until the mean temperature (averaged over a cycle) of checker and gas streams remains unchanged from cycle to cycle. An algorithm for universal computation is set up for the most complex case of regenerators operating with through and loop coils, with triple blast. For each specific case appropriate simplifying assumptions are made. In the calculations the influence of water vapor, the heat supply from the surrounding medium, and the varying heat capacities of flows and checker are taken into account.