Most of the dynamic optimal control problems in chemical engineering can be written in the form of differential algebraic equations (DAEs).Simultaneous approach is an important method for solving these problems.The discretization strategies often used in this approach are local methods

for instance

orthogonal collocation on finite elements (OCFE)

which has many advantages.Pseudo-spectral (PS)

as a global method

has its own unique properties.It may offer a rapid convergence rate for the approximation of analytic functions and has high precision and low computational effort with a simple structure.As the representations of local method and global method respectively

OCFE and PS were compared.The collocation points and their different distributions were presented

and the degree of freedom (DOF) of non-linear programming (NLP) after discretization was discussed

as well as the criteria were offered to ensure the DOF of the NLPs.At last

a continuous case and a discontinuous case were studied

and it was concluded that if the problem was smooth enough then the convergence of PS was better than that of OCFE.