A Review: Differential Transform Method for Semi-Analytical Solution of Differential Equations

M.M. Rashidi 1 , F. Rabiei 2 , S. Naseri Nia 2  and S. Abbasbandy 3
  • 1 Shanghai Automotive Wind Tunnel Center, Tongji University, Shanghai, China
  • 2 School of Engineering, Monash University Malaysia, Selangor, Malaysia
  • 3 Department of Applied Mathematics, Imam Khomeini International University, Qazvin

Abstract

In this article, the semi-analytical method known as the Differential Transform Method (DTM) for solving different types of differential equations is reviewed. First, basic definitions and formulas of DTM and Differential Transform-Padé approximation (DTM-Padé), which are used to increase the convergence and accuracy of DTM approximations, are discussed. Then both techniques of DTM and DTM-Padé, which have been successfully applied to partial differential equations, as well as the application of these methods in fluid mechanic and heat transfer are presented. In addition, the extension of DTM for integral differential equations and the fuzzy differential transformation method (FDTM) for fuzzy problems are discussed.

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