The Estimation of Rate Constants in Systems of Linear and Nonlinear Differential Equations Using the Polynomial-approximated Least Squares-error and Iterative Search Technique

Abstract

A new technique is proposed for estimating the rate constants in systems of linear or nonlinear differential equations, using a polynomial approximation of the observed concentrations of species participating in the reaction and an iterative search technique. The method is implemented by minimizing the errors of the concentrations (of species), as computed by the theoretical equations derived from the linear differential equations or by the trapezoidal averaging simulation, relative to those calculated by the polynomial approximation. The present technique requires the concentrations (at the initial reaction stage) of s-2 species (the s species takes part in the reaction). Two kinetic example, A\ightleftarrowsB\ightleftarrowsC and S+E\ightleftarrowsES→P, have been used to illustrate and develop the present technique.