Abstract
In this article, we implement a spectral collocation methodby usingthe properties of Legendre and Lagrange polynomials for solving the resulting nonlinear system of ODEs of the biochemical reaction model. This technique reduces the proposed model to a system of algebraic equations. We prove the uniqueness and present the local stability of the given model. A comparison with the numerical solutionis obtained by using the RK4method and thepreviouslypublished results using the Picard-Pade method. The proposed method introduces a promising tool for solving many nonlinearsystemsof differential equations. Numerical illustrations are stated to demonstrate utility, validity and the great potential of the introduced method.