Solutions of delay differential equations by using differential transform method

Karakoç, Fatma; Bereketoğlu, Hüseyin

doi:10.1080/00207160701750575

Cited by 50 publications

(44 citation statements)

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“…Most of these equations have no analytical solution and so, numerical methods may be required to obtain their approximate solutions [9][10][11][12][13]. For this reason, the Laguerre collocation method has been presented.…”

Section: Discussionmentioning

confidence: 99%

“…In recent years, it is well known that there exists an increasing interest in the application of the models to nonlinear problems in biology, physics and engineering. Also, the numerical solution methods of problems of these types have been developed very rapidly and intensively by many authors [1][2][3][4][5]. Here, the basic ideas of the mentioned studies are developed and applied to the high-order nonlinear ordinary differential equations in the form …”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Laguerre Polynomial Solutions of a Class of Initial and Boundary Value Problems Arising in Science and Engineering Fields

Gürbüz

Sezer

2016

Acta Phys. Pol. A

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In this study, we consider high-order nonlinear ordinary differential equations with the initial and boundary conditions. These kinds of differential equations are essential tools for modelling problems in physics, biology, neurology, engineering, ecology, economy, astrophysics, physiology and so forth. Each of the mentioned problems are described by one of the following equations with the specific physical conditions: Riccati, Duffing, EmdenFowler, Lane Emden type equations. We seek the approximate solution of these special differential equations by means of a operational matrix technique, called the Laguerre collocation method. The proposed method is based on the Laguerre series expansion and the collocation points. By using the method, the mentioned special differential equations together with conditions are transformed into a matrix form which corresponds to a system of nonlinear algebraic equations with unknown Laguerre coefficients, and thereby the problem is approximately solved in terms of Laguerre polynomials. In addition, some numerical examples are presented to demonstrate the efficiency of the proposed method and the obtained results are compared with the existing results in literature.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Laguerre Polynomial Solutions of a Class of Initial and Boundary Value Problems Arising in Science and Engineering Fields

Gürbüz

Sezer

2016

Acta Phys. Pol. A

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“…It's worth pointing out that, using the method given in [13], only approximate solution can be obtained. On the other hand, for DDEs (3), the initial function has the vital role.…”

Section: Y T Y T T T Y T T Tmentioning

confidence: 99%

“…There are many papers devoted to the problem of approximate solution of DDEs [9]- [15]. Recently, F. Karako and H. Bereketoğlu [13] extend the method of differential transformation for solving the following two types of DDEs:…”

Section: Introductionmentioning

confidence: 99%

Differential Transform Method for Some Delay Differential Equations

Liu¹,

Zhou²,

Du³

2015

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“…equations containing shifts of the unknown function are developed very rapidly and intensively. It is well known that linear delay difference equations have been considered by many authors [1][2][3][4][5][6][7][8][9][10][11]. The past couple decades have seen a dramatic increase in the application of delay models to problems in biology, physics and engineering [12][13][14][15].…”

Section: Introductionmentioning

confidence: 99%