Implementation of the solution algorithms for index and near index problems

Abstract: "This paper deals with implementing the solution algorithm for index and near index problems proposed by Chung and Westerberg. A numerical singularity checking method is suggested to detect the singularity or the near singularity of a matrix and to identify the equations responsible for the singularity or near singularity. An exact numerical differentiation method is also suggested to generate elements of the Jacobian matrix and the equations needed. The potential use of the existing algebraic equation and ODE/DAE solvers in constructing a solver for index and near index problems is also studied. With the numerical method suggested in this paper, index and near index problems can be numerically and automatically solved."