The differential transformation method (DTM) is an alternative procedure for obtaining an analytic Taylor series solution of differential equations. The main advantage of this method is that it can be applied directly to nonlinear differential equations without requiring linearization and discretization, and therefore, it is not affected by errors associated with discretization. The concept of DTM was first introduced to solve linear and nonlinear problems in electrical circuits. This chapter introduces DTM generally and contains the following:
1.1
Introduction
1.2
Principle of Differential Transformation Method
1.3
Multistep Differential Transformation Method
1.4
Hybrid Differential Transformation Method and Finite Difference Method
1.5
Differential Transformation Method Applying on Initial-Value Problems and Ordinary Differential Equations
1.6
Two-Dimensional Differential Transformation Method for Partial Differential Equations
1.7
Differential Transformation Method–Padé Approximation
1.8
DTM-Padé Approximation on Singular Two-Point Boundary Value Problem
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