An improved method based on Legendre computational matrix method for time dependent Michaelis-Menten enzymatic reaction model arising in mathematical chemistry
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A mathematical model of dynamic form of the Michaelis-Menten enzy- matic reaction model is discussed. In this paper, we have applied Legendre spectral algorithm for solving the time dependent Michaelis-Menten enzy- matic reaction equations. To the best of our knowledge until there is no rigorous Legendre wavelet solution has been reported for the above men- tioned model. From the Legendre spectral solutions, we are then able to analyze the efficiency of the enzymatic reaction model parameters on the solutions to the dynamic Michaelis-Menten enzymatic reaction equations. The numerical results demonstrate the accuracy and efficiency of the pro- posed spectral approach. The Legendre computational matrix method (LCMM) is shown to be a rather useful and efficient tool for constructing analytical solutions to the dynamic Michaelis-Menten enzymatic reaction equations. Convergence analysis of the proposed method is discussed. Some illustrative examples are given to demonstrate the validity and ap- plicability of the proposed method.
Abstract
A mathematical model of dynamic form of the Michaelis-Menten enzy- matic reaction model is discussed. In this paper, we have applied Legendre spectral algorithm for solving the time dependent Michaelis-Menten enzy- matic reaction equations. To the best of our knowledge until there is no rigorous Legendre wavelet solution has been reported for the above men- tioned model. From the Legendre spectral solutions, we are then able to analyze the efficiency of the enzymatic reaction model parameters on the solutions to the dynamic Michaelis-Menten enzymatic reaction equations. The numerical results demonstrate the accuracy and efficiency of the pro- posed spectral approach. The Legendre computational matrix method (LCMM) is shown to be a rather useful and efficient tool for constructing analytical solutions to the dynamic Michaelis-Menten enzymatic reaction equations. Convergence analysis of the proposed method is discussed. Some illustrative examples are given to demonstrate the validity and ap- plicability of the proposed method.
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