The Differential Transform Method as an Effective Tool to Solve Implicit Hessenberg Index-3 Differential-Algebraic Equations

Differential-algebraic equations (DAEs) are important tools to model complex problems in various application fields easily. Those DAEs with an index-3, even the linear ones, known cause when solving them numerically. The present article proposes a new algorithm together its multistage form efficiently solve class of nonlinear implicit Hessenberg index-3 DAEs. This is based on idea applying differential transform method (DTM) directly DAE without traditional index reduction methods, which can be and often result violations constraints. Also, deal terms DAE, we approximate using Adomian polynomials. has given us simple efficient algorithm, involves solution algebraic systems except for initial recursion terms. easy implement Maple or Mathematica. Furthermore, enlarge interval convergence power series obtained from DTM, DTM also given. Both algorithms applied two examples highly Numerical results show that determine exact convergent series, while compute accurate numerical solutions over large intervals.