Solution of non-linear initial value problems by the orthogonal collocation method

Abstract

The mathematical model of the plug flow tubular reactor (PFTR) in steady state behavior, consisting of a set of initial value ordinary differential equations, is solved by the orthogonal collocation method. The solution to the resulting set of non-linear collocation equations is found by the Newton-Raphson iteration formula, as well as by a method of successive approximations. The computation time required by both techniques for given accuracy is studied as a function of the number of collocation points, the number of subdivisions of the integration interval and the number of differential equations, The method of successive approximations becomes more powerful than the Newton-Raphson technique for larger numbers of differential equations.