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

Algorithm 2

MsDTM algorithm.

(1)	Choose the number of subdivisions and the order of approximation .
(2)	Subdivide the interval into equal subintervals , of size where .
(3)	Let , apply the DTM to the DAE (1) on using and to obtain the approximate solution , , and , .
(4)	From until , apply the DTM to DAE (1) on using and to obtain the approximate solutions , , and , .
(5)	Repeat step 4.
(6)	An approximate solution to the DAE initial-value problems (1) and (2) on is given by
	and