Orthogonal collocation for the analysis of immobilized enzyme systems

Abstract

Orthogonal collocation method is applied to the analysis of nonlinear ordinary differential equations containing Michaelis—Menten kinetics. The solution is expanded in a series of Lagrange interpolation polynomials and Gauss—Jacobi quadratures are used in calculating effectiveness factors. A set of nonlinear algebraic equations resulting from collocation approximation is conveniently solved by the Gauss—Seidel iterative method, but its convergence path is not monotonous. Although the rate of convergence depends on system parameters, orthogonal collocation is more efficient than the Runge—Kutta method in solving boundary value problems even at a high Thiele modulus.