The modified algorithm for the differential transform method to solution of Genesio systems

Gökdoğan, Ahmet; Merdan, Mehmet; Yıldırım, Ahmet

doi:10.1016/j.cnsns.2011.03.039

Cited by 57 publications

(35 citation statements)

References 38 publications

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“…(11a), (11b), (11c), (13a), and(13b). Because this technique has been presented in detail by several investigators (Ames, 2014;Bieniasz, 2015;Gökdoğan, Merdan, & Yildirim, 2012), only some pertinent steps in solving are outlined in this paper. Additionally, since Eqs.…”

Section: Analytical Solutionmentioning

confidence: 99%

Transport of solutes under transient flow conditions – A case study – Yamuna river sub basin (Kosi Kalan to Agra)

Kumar

Sharma

Rani

2015

International Soil and Water Conservation Research

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The imbalance between incoming and outgoing salt causes salinization of soils and sub-soils that result in increasing the salinity of stream-flows and agriculture land. This salinization is a serious environmental hazard particularly in semi-arid and arid lands. In order to estimate the magnitude of the hazard posed by salinity, it is important to understand and identify the processes that control salt movement from the soil surface through the root zone to the ground water and stream flows. In the present study, Yamuna sub-basin (both sides of Gokul dam site) has been selected which has two distinct climatic zones, sub-humid (upstream of Mathura) and semi-arid region (downstream of Mathura). In the upstream, both surface and ground waters are used for irrigation, whereas in the downstream mostly groundwater is used. Both soils and ground waters are more saline in downstream parts of the study area. In this study we characterized the soil salinity and groundwater quality in both areas. An attempt is also made to model the distribution of potassium concentration in the soil profile in response to varying irrigation conditions using the Soil-Water Infiltration and Movement (SWIM) model. Fair agreement was obtained between predicted and measured results indicating the applicability of the model.

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Section: Analytical Solutionmentioning

confidence: 99%

Transport of solutes under transient flow conditions – A case study – Yamuna river sub basin (Kosi Kalan to Agra)

Kumar

Sharma

Rani

2015

International Soil and Water Conservation Research

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“…In [16], a promising technique was presented to calculate the transformed functions of nonlinear functions with one variable by using the Adomian polynomials. Secondly, those works [22,37,45] which aim to improve the accuracy of the DTM have extended the applications of this method. Actually, in the past 40 years, the DTM and its modifications have been successfully applied to solve various differential equations [6,14,17,22,37,38,40,45,51], difference equations [3], differential-difference equations [4], integral equations [5,44,50] and integrodifferential equations [2,5].…”

Section: Introductionmentioning

confidence: 98%

A new algorithm based on differential transform method for solving multi-point boundary value problems

Xie

Zhou

2015

International Journal of Computer Mathematics

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In this work, an efficient algorithm based on the differential transform method is applied to solve the multi-point boundary value problems. The solution obtained by using the proposed method takes the form of a convergent series with easily computable components. Several numerical examples, both linear and nonlinear, are given to testify the validity and applicability of the proposed method. Comparisons are made between the present method and the other existing methods.

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“…Their results derived by differential transform method were compared with the results of homotopy analysis method and Adomian decomposition method and it was shown that DTM used for quadratic Riccati differential equation was more effective and promising than homotopy analysis method and Adomain decomposition method. Gokdogan et al [7] acquired an approximate analytical solution of chaotic Genesio system by the modified differential transform method. Ayaz [8] has studied two-dimensional differential transform method of solution of the initial value problem for partial differential equations (PDEs).…”

Section: Introductionmentioning

confidence: 99%

Propulsion and launching analysis of variable-mass rockets by analytical methods

Ganji

Gorji

Hatami

et al. 2013

Propulsion and Power Research

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In this study, applications of some analytical methods on nonlinear equation of the launching of a rocket with variable mass are investigated. Differential transformation method (DTM), homotopy perturbation method (HPM) and least square method (LSM) were applied and their results are compared with numerical solution. An excellent agreement with analytical methods and numerical ones is observed in the results and this reveals that analytical methods are effective and convenient. Also a parametric study is performed here which includes the effect of exhaust velocity (C e ), burn rate (BR) of fuel and diameter of cylindrical rocket (d) on the motion of a sample rocket, and contours for showing the sensitivity of these parameters are plotted. The main results indicate that the rocket velocity and altitude are increased with increasing the C e and BR and decreased with increasing the rocket diameter and drag coefficient.

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The modified algorithm for the differential transform method to solution of Genesio systems

Cited by 57 publications

References 38 publications

Transport of solutes under transient flow conditions – A case study – Yamuna river sub basin (Kosi Kalan to Agra)

Transport of solutes under transient flow conditions – A case study – Yamuna river sub basin (Kosi Kalan to Agra)

A new algorithm based on differential transform method for solving multi-point boundary value problems

Propulsion and launching analysis of variable-mass rockets by analytical methods

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