Numerical Solution of the Direct Problem in Chemical Kinetics

Abstract

Previously discussed analytical methods for solving the direct problem in chemical kinetics are not sufficient for analysis of different reaction kinetic schemes. First, even given the mathematical model represented by an ODE system, it is not always possible to integrate the equations analytically. The reason for that may be just an absence of such a solution. This refers primarily to a large number of kinetic models in which differential equations are non-linear relative to the sought functions. Second, if the analytical solution is obtained, it is often to lengthy and awkward. Finally, there is a large class of real mathematical models that are described by partial differential equation sets, which cannot be integrated numerically. Thus, the series of mathematical problems that can be solved with the previously discussed numerical integration methods is quite narrow. That is why, in order to solve the direct problem, we have to rely on more universal approaches. Such approaches are based on using numerical integration of differential equations and systems.