Stiffness‐Adaptive Taylor method for the integration of non‐stiff and stiff kinetic models

A systematic derivation procedure that greatly facilitates the application of the Taylor method to the integration of kinetic models is developed. In addition, an algorithm that gives the integration step as a function of the required level of accuracy is proposed. Using the Taylor method, application of this algorithm is immediate and largely reduces the integration time. In addition, a new method of integration of kinetic models, whose most important feature is the self‐adaptability to the stiffness of the system along the integration process, is developed. This “stiffness‐adaptive” Taylor method (SAT method) makes use of several algorithms, combining them to meet the particular requirements of the integration of each species along the integration process. In comparison with the Runge–Kutta–Felhberg, Runge–Kutta–Calahan, Taylor, and Gear methods, the SAT method is the best to integrate non‐stiff and stiff kinetic systems, giving the best accuracy and the smallest computing time.