Seyed Hamed Hashemi Mehne - Aerospace Research Institute, Tehran, Iran

The complexity of solving differential equations in real-world applications motivates researchers to extend numerical methods.  Among different numerical and semi-analytical methods for solving initial and boundary value problems, the differential transform method (DTM) has received notable attention.  It has developed and experienced generalizations for implementing other types of mathematical problems such as optimal control, calculus of variations, and integral equations. This review aims to provide insight into DTM.  History, theoretical base, applications, computational aspects, and its revisions are reviewed. The present study helps to understand the theory, capabilities, and features of the DTM, as well as its drawbacks and limitations.

Boundary value problems, Initial value problems, Differential Transform Method, Semi-analytical methods