### Computing the Low Dimension Manifold in Dissipative Dynamical Systems

#### Abstract

*The importance of the model reduction techniques cannot be denied or ignored for a number of combustion problems in chemical sciences. We examine an analysis of very well-known method by Mass and Pope by measuring the influence of physical processes on the water-gas shift reaction (WGSR). We observe that if the process of physical and chemical reactions is coupled, this will lead to a very dramatic effect. An adaptive parameterization technique is developed for the numerical implementation. Through proper algorithm and grid size variations, the approximate solution is obtained and further refined with the method of invariant grids. Consequently, it leads us to a vicious effect on CPU when we extended this idea to higher dimensions *

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