Differential Equation And Application In Enzyme Kinetics

In this paper, the applications of the differential transform method to solving the nonlinear equation and the applications of the characteristic set method to the enzyme dynamic system were discussed.The first chapter, we introduced the development of enzyme kinetics, including the history, the background, the current research situation, and so on. Then we briefly introduced the mathematics mechanization and the reduced differential transform method(RDTM). At last, we gave the main results in this paper.The second chapter was the preliminary knowledge. Some definitions and theorems was included, such as the order relation, polynomial reduced, affine clusters, characteristic set and its applications, etc.In the third chapter, we discussed the use of differential transform method (RDTM) in solving the nonlinear differential equation. By solving the Burgers equation and other nonlinear evolution equation, we can see that compared to ADM,VIM and DTM, RDTM is much more accurate and convenient. What's more, any requirement were not needed by RDTM to get the approximate solutions. Such as special transformations, linearization or discretization.In the forth chapter, the application of characteristic set method in the enzyme dynamic system was discussed. We analyzed the simplest enzymatic reaction which only included one product, one enzyme, and one compound. Under the assumption that the initial concentration of enzyme is far greater than the initial concentration of the substrate, we transformed the reaction system of nonlinear equations into linear equations system. Then the linear equations system was solved with the computing arithmetic software MAPLE, obtained the functions of the relations between the concentration of the substrate, product and the compound with time. At last, we select the exact value to draw the figures, and the figures illustrated the rationality of the method.