The differential transform approximation for the system of ordinary differential equations

Kurnaz, Aydın; Oturanç, Galip

doi:10.1080/00207160512331329050

Cited by 42 publications

(25 citation statements)

References 8 publications

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“…The results obtained by Taylor collocation method compared with the results of differential transform method [8] and Adomian decomposition method [7,9] ( Fig. 1).…”

Section: Taylor Collocation Methodsmentioning

confidence: 93%

The Maple Program Procedures at Solution Systems of Differential Equation with Taylor Collocation Method

Servi

Keskin

Oturanç

2014

Springer Proceedings in Mathematics &Amp; Statistics

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In this paper, a maple algorithm Taylor collocation method has been presented for numerically solving the systems of differential equation with variable coefficients under the mixed conditions. The solution is obtained in terms of Taylor polynomials. This method is based on taking the truncated Taylor series of the function in equations and then substituting their matrix forms in the given equation. Hence, the result of matrix equation can be solved and the unknown Taylor coefficients can be found approximately. The results obtained by Taylor collocation method will be compared with the results of differential transform method and Adomian decomposition method.

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“…The results obtained by Taylor collocation method compared with the results of differential transform method [8] and Adomian decomposition method [7,9] ( Fig. 1).…”

Section: Taylor Collocation Methodsmentioning

confidence: 93%

The Maple Program Procedures at Solution Systems of Differential Equation with Taylor Collocation Method

Servi

Keskin

Oturanç

2014

Springer Proceedings in Mathematics &Amp; Statistics

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“…Afterwards, it was applied to several systems and differential equations. For instance, initial -value problems [10], difference equations [11], integro-differential equations [12], partial differential equations [13,14], system of ordinary differential equations [15]. Definition 1.…”

Section: Differential Transformation Methodsmentioning

confidence: 99%

“…Definition 1. The one-dimensional differential transform of a function y(x) at the point 0 x x  is defined as follows [8,15]:…”

Section: Differential Transformation Methodsmentioning

confidence: 99%

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The Differential Transformation Method and Pade Approximant for a Form of Blasius Equation

Peker

Karaoğlu

Oturanç

2011

MCA

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Abstract-Boundary conditions in an unbounded domain, i.e. boundary condition at infinity, pose a problem in general for the numerical solution methods. The aim of this study is to overcome this difficulty by using Padé approximation with the differential transform method (DTM) on a form of classical Blasius equation. The obtained results are compared with, for the first time, the ones obtained by using a modified form of Adomian decomposition method (ADM). Furthermore, in order to see the consistency of solutions, they are also compared with the ones obtained by using variational iteration method (VIM).

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“…The technique that we used here is the differential transform (DT) method [3,5,8,9,13,16], which is based on the Taylor series expansion. It gives exact values of the nth derivative of an analytical function at a point in terms of known and unknown boundary conditions in a fast manner.…”

Section: Introductionmentioning

confidence: 99%

Numerical implementation of differential transformations method for integro-differential equations

Özkan

2010

International Journal of Computer Mathematics

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Differential transformation (DT) is one of the numeric methods for solving differential equations. The advantage of this method is to transform the differential equation into algebraic ones. The aim of this article is to present a comparative study of the DT for solving of linear or nonlinear integro-differential equations. A remarkable practical feature of this method is its ability to solve integro-differential equations efficiently. This method also enable us to control truncation error by adjusting the step size used in the numerical scheme. Numerical examples are used to illustrate the preciseness and effectiveness of the proposed method.

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The differential transform approximation for the system of ordinary differential equations

Cited by 42 publications

References 8 publications

The Maple Program Procedures at Solution Systems of Differential Equation with Taylor Collocation Method

The Maple Program Procedures at Solution Systems of Differential Equation with Taylor Collocation Method

The Differential Transformation Method and Pade Approximant for a Form of Blasius Equation

Numerical implementation of differential transformations method for integro-differential equations

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