Economised Power Series Solutions of Differential-Algebraic Equations with Hessenberg Index-2 by Legendre Approximation.

The numerical solution of differential- algebraic equations with Hessenberg Index-2 using the Legendre polynomial approximation is presented. We use are used to approximate the power series solutions of the resulting system of equations evolving from the DAEs. Some numerical examples were tested and absolute errors of the computation obtained to establish the order of accuracy. The results show at least order six accuracy for a system of DAEs. It is however more desirable for systems of index-1 DAEs than a singly-formulated DAE in terms of stability properties.