Theory and application of orthogonal collocation on the modeling of chemical reacting systems

A unified computer package for solving differential equations has been designed based on the orthogonal collocation numerical methods. This package is extremely efficient and easy to use for setting up the collocation constants, solving systems of nonlinear algebraic equations, integrating stiff differential equations and estimating parameters in equations that arise from discretization of differential equations by orthogonal collocation. Guidelines for choosing optimal polynominals and quadrature formulae and for evaluation of collocation constants are suggested. Three numerical examples taken from chemical reaction engineering are used to demonstrate the mechanics and powerful features of this method. Mathematical models that describe consecutive enzymatic reactions with deactivation by one reaction product are developed. Results indicate that diffusional modification plays a strong role in the kinetic behavior of these types of reaction. Orthogonal collocation is also applied to estimate the kinetic parameters of a first order reaction inside a two-dimensional tubular flow reactor. Based on the optimal choices of polynominals and of the quadrature formula suggested here, more accurate estimates are obtained for both totally and partially observed systems than in previous investigations. [...]