<i>n</i>-Dimensional differential transformation method for solving PDEs

Kurnaz, Aydın; Oturanç, Galip; Ki̇ri̇ş, Mehmet Eyüp

doi:10.1080/0020716042000301725

Cited by 77 publications

(45 citation statements)

References 8 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Regarding the preceding equation, one can immediately recognize the simplicity inher- (1083) ent in the denition of the inverse dierential transform. We skip the details on the denitions/properties of the n-dimensional dierential transform and refer the interested reader to [14]. A number of fundamental operations of the one-dimensional dierential transform are given in Appendix A, Table A.1. Most recently, Fatoorehchi and Abolghasemi [11] have managed to extend the DTM to nonlinear functional equations of arbitrary types.…”

Section: Preliminaries Of the Improved Dierential Transform Methodsmentioning

confidence: 99%

An Explicit Analytic Solution to the Thomas-Fermi Equation by the Improved Differential Transform Method

Fatoorehchi

Abolghasemi

2014

Acta Phys. Pol. A

View full text Add to dashboard Cite

In this paper, a newly proposed analytical scheme by the authors namely the improved dierential transform method is employed to provide an explicit series solution to the ThomasFermi equation. The solution procedure is very straightforward, requiring merely elementary operations together with dierentiation, and ends up in a recursive formula involving the Adomian polynomials to aord the unknown coecients. Unlike many other methods, our approach is free of integration and hence can be of computational interest. In addition, a very good agreement between the proposed solution and the results from several well-known works in the literature is demonstrated.

show abstract

Section: Preliminaries Of the Improved Dierential Transform Methodsmentioning

confidence: 99%

An Explicit Analytic Solution to the Thomas-Fermi Equation by the Improved Differential Transform Method

Fatoorehchi

Abolghasemi

2014

Acta Phys. Pol. A

View full text Add to dashboard Cite

show abstract

“…Similarly, Example 1 in [27] follows as a special case of our general solution (27) by substituting n = 4 and α = 1. Example 5.2.…”

Section: Example 51 Consider the Following N-dimensional Heat-like mentioning

confidence: 99%

“…Various applications of DTM are given in [22 -26]. Recently Kurnaz et al [27] have applied DTM for solving partial differential equations. Arikoglu and Ozkol [28] developed the fractional differential transform method which is based on the classical differential transform method, on fractional power series, and on Caputo fractional derivatives.…”

Section: Introductionmentioning

confidence: 99%

Analytic Solution of Fractional-Order Heat- and Wave-Like Equations Using Generalized n-dimensional Differential Transform Method

Baranwal

Pandey

Tripathi

et al. 2011

Zeitschrift Für Naturforschung A

View full text Add to dashboard Cite

In this paper, we have introduced a generalized n-dimensional differential transform method to propose a user friendly algorithm to obtain the closed form analytic solution for n-dimensional fractional heat-and wave-like equations. Three examples are given to establish the simplicity of the algorithm. In Example 5.3, we show that ten terms of the series representing the solution, even in fractional order, give a very accurate solution.

show abstract

“…Since the main advantage of this method is that it can be applied directly to nonlinear ordinary and partial differential equations without requiring linearization, discretization or perturbation, it has been studied and applied during the last two decades widely. DTM has been used to obtain numerical and analytical solutions of ordinary differential equations [3], partial differential equations [4], eigenvalue problems [5], differential algebraic equations [6] [7], integral equations [8] and so on.…”

Section: Introductionmentioning

confidence: 99%