scholarly journals A Cumulative Study on Differential Transform Method

2019 ◽  
Vol 4 (1) ◽  
pp. 170-181 ◽  
Author(s):  
Geeta Arora ◽  
Pratiksha
Keyword(s):  
Differential Equation ◽  
Power Series ◽  
Differential Equations ◽  
Exact Solutions ◽  
Real World ◽  
Analytical Methods ◽  
Analytic Solutions ◽  
Differential Transform Method ◽  
Transform Method ◽  
Differential Transform

Many real-world phenomena when modelled as a differential equation don't generally have exact solutions, so their numerical or analytic solutions are sought after. Differential transform method (DTM) is one of the analytical methods that gives the solution in the form of a power series. In this paper, a cumulative study is done on DTM and its evolution as an effective method to solve the gamut of differential equations.

scholarly journals Using the Differential Transform Method to Solve Non-Linear Partial Differential Equations

2020 ◽  
pp. 34-43
Author(s):  
Fadwa A. M. Madi ◽  
Fawzi Abdelwahid
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Exact Solutions ◽  
Variable Coefficients ◽  
Differential Transform Method ◽  
Partial Differential ◽  
Transform Method ◽  
Linear Partial Differential Equations ◽  
Differential Transform ◽  
Non Linear

In this work, we reviewed the two-dimensional differential transform, and introduced the differential transform method (DTM). As an application, we used this technique to find approximate and exact solutions of selected non-linear partial differential equations, with constant or variable coefficients and compared our results with the exact solutions. This shows that the introduced method is very effective, simple to apply to linear and nonlinear problems and it reduces the size of computational work comparing with other methods.

scholarly journals Exact solutions for the differential equations in fractal heat transfer

2016 ◽  
Vol 20 (suppl. 3) ◽  
pp. 747-750 ◽  
Author(s):  
Chun-Yu Yang ◽  
Yu-Dong Zhang ◽  
Xiao-Jun Yang
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Exact Solutions ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Differential Transform Method ◽  
Transform Method ◽  
Differential Transform ◽  
Fractional Differential

In this article we consider the boundary value problems for differential equations in fractal heat transfer. The exact solutions of non-differentiable type are obtained by using the local fractional differential transform method.

scholarly journals Modified Differential Transform Method for Solving Vibration Equations of MDOF Systems

2016 ◽  
Vol 2 (4) ◽  
pp. 123-139 ◽  
Author(s):  
Mohammadamir Najafgholipour ◽  
Navid Soodbakhsh
Keyword(s):  
Differential Equations ◽  
Exact Solutions ◽  
Degrees Of Freedom ◽  
Computational Cost ◽  
Method Comparison ◽  
Differential Transform Method ◽  
System Of Differential Equations ◽  
Transform Method ◽  
Mdof Systems ◽  
Differential Transform

Vibration equations of discrete multi-degrees-of-freedom (MDOF) structural systems is system of differential equations. In linear systems, the differential equations are also linear. Various analytical and numerical methods are available for solving the vibration equations in structural dynamics. In this paper modified differential transform method (MDTM) as a semi-analytical approach is generalized for the system of differential equations and is utilized for solving the vibration equations of MDOF systems. The MDTM is a recursive method which is a hybrid of Differential Transform Method (DTM), Pade' approximant and Laplace Transformation. A series of examples including forced and free vibration of MDOF systems with classical and non-classical damping are also solved by this method. Comparison of the results obtained by MDTM with exact solutions shows good accuracy of the proposed method; so that in some cases the solutions of the vibration equation that found by MDTM are the exact solutions. Also, MDTM is less expensive in computational cost and simpler with compare to the other available approaches.

scholarly journals Modified Differential Transform Method for Two Singular Boundary Values Problems

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Yinwei Lin ◽  
Hsiang-Wen Tang ◽  
Cha’o-Kuang Chen
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Numerical Solutions ◽  
Nonlinear Models ◽  
Differential Transform Method ◽  
Singular Boundary ◽  
Boundary Values ◽  
Transform Method ◽  
Differential Transform ◽  
Linear And Nonlinear

This paper deals with the two singular boundary values problems of second order. Two singular points are both boundary values points of the differential equation. The numerical solutions are developed by modified differential transform method (DTM) for expanded point. Linear and nonlinear models are solved by this method to get more reliable and efficient numerical results. It can also solve ordinary differential equations where the traditional one fails. Besides, we give the convergence of this new method.

scholarly journals Modified differential transform method for solving linear and nonlinear pantograph type of differential and Volterra integro-differential equations with proportional delays

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Seyyedeh Roodabeh Moosavi Noori ◽  
Nasir Taghizadeh
Keyword(s):  
Exact Solution ◽  
Differential Equations ◽  
Differential Transform Method ◽  
Hybrid Technique ◽  
Transform Method ◽  
Proportional Delays ◽  
Differential Transform ◽  
Computational Work ◽  
Linear And Nonlinear ◽  
First Time

AbstractIn this study, a hybrid technique for improving the differential transform method (DTM), namely the modified differential transform method (MDTM) expressed as a combination of the differential transform method, Laplace transforms, and the Padé approximant (LPDTM) is employed for the first time to ascertain exact solutions of linear and nonlinear pantograph type of differential and Volterra integro-differential equations (DEs and VIDEs) with proportional delays. The advantage of this method is its simple and trusty procedure, it solves the equations straightforward and directly without requiring large computational work, perturbations or linearization, and enlarges the domain of convergence, and leads to the exact solution. Also, to validate the reliability and efficiency of the method, some examples and numerical results are provided.

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