A system and method for simulating a mechanistic kinetic process, such as a chemical process including one or more chemical reactions, over a predetermined time period, subject to a programmed temperature variation, is provided. The simulation proceeds stochastically, by taking discrete time steps through the time period. The time steps vary in size, based on instantaneous reaction rate values for the reactions taking place. Reaction rates can vary by many orders of magnitude, and sometimes a stochastically calcualated time step will be so great that it might skip over a later increase in chemical activity. To avoid loss of accuracy and control of the simulation due to such excessively large time steps, when the stochastically determined time step exceeds a threshold, one or more smaller, deterministic time steps are made. The deterministic time steps "inch" forward in time, until an increase in chemical activity is detected. Then, stochastic time steps are resumed. In this manner, a simulation according to the invention detects and simulates the increase in activity. The invention more broadly covers any simulation over an interval of values for an independent state variable (e.g., time), where there are one or more programmed state variables (e.g., temperature, pressure, etc, expressed as a function of the independent state variable). Time steps are made based on a process parameter (related to the instantaneous reaction rates or probabilities of occurrence), whose value is related to a current system state related to the current programmed state variable values (e.g. , temperature- dependent reaction rates).
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