Slow manifolds in chemical kinetics

Modelling the chemical system, especially for complex and higher dimensional problems, gives an easy way to handle the ongoing reaction process with respect to time. Here, we will consider some of the newly developed computational methods commonly used for model reductions in a chemical reaction. An effective (simple) method is planned to measure the low dimensional manifold, which reduces the higher dimensional system in such a way that it may not affect the precision of the whole mechanism. The phase flow of the solution trajectories near the equilibrium point is observed while the initial approximation is measured with the spectral quasi equilibrium manifold, which starts from the equilibrium point. To make it an invariant curve, the approximated curve is first refined a certain number of times using the method of invariant grids. The other way of getting the reduced data in the low dimensional manifold is possible through the intrinsic low dimensional manifold. Then, we compare these two invariant curves given by both the methods. Finally, the idea is extended to the higher dimensional manifold, where more number of progress variables will be added. (author)