numerical solution of higher index daes using theiriae's structure: trajectory-prescribed path controlproblem and simple pendulum

In this paper, we solve higher index differential algebraic equations (daes) by transforming them into integral algebraic equations (iaes). we apply collocation methods on continuous piecewise polynomials space to solve the obtained higher index iaes. the efficiency of the given method is improved by using a recursive formula for computing the integral part. finally, we apply the obtained algorithm to solve a trajectory-prescribed path control problem and a model of simple pendulum. the numerical experiments show efficiency of the given techniques.