Differential transform method: Acomprehensive review and analysis

The complexity of solving differential equations in real-world applicationsmotivates researchers to extend numerical methods. among differentnumerical and semi-analytical methods for solving initial and boundaryvalue problems, the differential transform method (dtm) has received notableattention. it has developed and experienced generalizations for implementingother types of mathematical problems such as optimal control,calculus of variations, and integral equations. this review aims to provideinsight into dtm. history, theoretical base, applications, computationalaspects, and its revisions are reviewed. the present study helps to understandthe theory, capabilities, and features of the dtm, as well as itsdrawbacks and limitations.