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

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.

Metode Transformasi Diferensial untuk Menentukan Solusi Persamaan Diferensial Linier Nonhomogen

“…Metode ini adalah metode numerik semi analitik untuk menyelesaikan persamaan diferensial. Metode transformasi diferensial didasarkan pada ekspansi deret Taylor, yaitu solusinya dinyatakan dalam deret polinomial [3]. Keunggulan metode ini adalah mudah digunakan, dimana solusi dari persamaan diferensial biasa dan parsial dapat dicari dengan menggunakan teorema-teorema yang berlaku.…”

“…Keunggulan metode ini adalah mudah digunakan, dimana solusi dari persamaan diferensial biasa dan parsial dapat dicari dengan menggunakan teorema-teorema yang berlaku. Berdasarkan kajian [3] perbandingan kedekatan solusi numerik semi-analitik menggunakan metode transformasi diferensial dengan solusi analitiknya terlihat bahwa solusi yang diperoleh menggunakan metode transformasi diferensial memiliki tingkat kekonvergenan yang cepat terhadap solusi analitiknya.…”

MHD Nanofluid boundary layer flow over a stretching sheet with viscous, ohmic dissipation

“…The DTM has been explored and applied to a variety of linear and nonlinear issues in recent years. Rashidi et al [19] explored a DTM method for solving both linear and nonlinear differential equations. Mujammad et al [20] illustrated the DTM technique for unsteady nanoliquid flow and heat transfer.…”

“…We made an assumption that the constant temperature was T W > T ∞ and that the constant temperature was C W > C ∞ . The governing equations for the boundary layer, which include momentum, energy, and concentration equations with dissipation effects are as follows [19,24]…”

A Singularly P-Stable Multi-Derivative Predictor Method for the Numerical Solution of Second-Order Ordinary Differential Equations

“…Speed, accuracy, and precision are the most common evaluation metrics used to evaluate these numerical solutions. Due to significant advances in the processing capabilities and speed of the processors and computers in the late 20th century, numerical solutions became more prevalent and continue to expand [22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39]. The main topic presented in this paper is about the approximate solution of the following equation: y = f (x, y), y(x 0 ) = y 0 , y (x 0 ) = y 0 , (1) where f is a sufficiently continuous and derivative function of any order.…”