A new approach for computing the exact solutions of DAEs in generalized Hessenberg forms

‎In this paper‎, ‎we propose a new method‎, ‎with different approach and economical computing‎, ‎that presents explicit formulas for the exact solutions of a large class DAEs in Hessenberg forms‎. ‎First‎, ‎we illustrate the method for linear time-varying DAEs in Hessenberg forms‎, ‎in order to show the different approach and also we present an algorithm for proposed method that shows the method is as economic as possible‎. ‎Then‎, ‎we describe that the method is efficient for larger classes including special case of non-linear DAEs in Hessenberg forms‎. ‎Some examples are presented to illustrate the proposed method‎.