On the integration of kinetic models using a high‐order taylor series method

Abstract

A general equation to derive kinetic models up to any order is given. This equation greatly facilitates the application of the Taylor series method to the integration of kinetic models up to very high orders. When dealing with non-stiff models, computing time is always reduced by increasing the integration order, at least up to the 20th order. When the model is stiff, the integration order should be optimized; however, a twelfth order is recommended to integrate weakly stiff models. The use of an algorithm which permits the immediate calculation of the integration step size required to maintain a given accuracy leads to further reductions in computing time. When implemented as recommended here, a high-order Taylor series method is more rapid and accurate than Runge-Kutta and predictor-corrector methods and can be advantageously used in combination with optimization methods to perform mechanism studies and in multicomponent kinetic determinations.