Synthesis of reciprocating engine cycles requires stepwise calculation of the charge state from point to point round the cycle. Calculation can proceed either by numerical integration of the differential form of the first law of thermodynamics, or by iterative solution of an explicit non-linear equation for one state parameter at the end of a step (embodying, of course, approximations to the integrated heat and mass transfers during the step). Evidence is presented that the iterative method is superior to integration by a fourth-order Runge-Kutta procedure.