Numerical simulation of generalized Hirota–Satsuma coupled KdV equation by RDTM and comparison with DTM

Abazari, Reza; Abazari, Malek

doi:10.1016/j.cnsns.2011.05.022

Cited by 68 publications

(40 citation statements)

References 22 publications

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“…To examine the accuracy and reliability of the present technique for the generalized Hirota-Satsuma coupled KdV equation, we can take the different initial values [1,3,11,30] u(x, 0) = 1 3…”

Section: Second Kind Initial Conditionsmentioning

confidence: 99%

“…Now, we take the Hirota-Satsuma coupled KdV equation (18), with the following initial conditions [1,3,11,30] u(x, 0) = 1 3…”

Section: First Kind Initial Conditionsmentioning

confidence: 99%

“…Also, the soliton solution for this equation is constructed by Fan [10]. In recent years generalized Hirota-Satsuma coupled KdV equation has been analyzed by many research workers with the aid of different schemes such as Jacobi-elliptic function technique [28], the projective Riccati equations technique [29], the Adomian decomposition technique [30], the homotopy perturbation approach [11], the homotopy analysis scheme [1] and the reduced differential transform technique [3]. In recent times nonlinear differential equations have been studied by many authors by such as Baskonus et al [7], Baskonus [8,9], Rashidi et al [31][32][33] and others.…”

Section: Introductionmentioning

confidence: 99%

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An efficient computational approach for generalized Hirota-Satsuma coupled KdV equations arising in shallow water waves

Gupta

Kumar

Singh

2017

Waves, Wavelets and Fractals

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Abstract:The aim of this letter is to present a numerical algorithm for generalized Hirota-Satsuma coupled KdV equations arising in unidirectional propagation of shallow water waves by using the homotopy analysis transform technique. The computational approach is the merged form of the homotopy analysis technique and Laplace transform scheme. The technique provides a series solution, which converges very fast, components are very easily calculated, and it does not require linearization or small perturbation. The numerical and graphical results derived by making use of proposed approach indicate that the scheme is very user friendly and easy to implement.

show abstract

Section: Second Kind Initial Conditionsmentioning

confidence: 99%

“…Now, we take the Hirota-Satsuma coupled KdV equation (18), with the following initial conditions [1,3,11,30] u(x, 0) = 1 3…”

Section: First Kind Initial Conditionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

An efficient computational approach for generalized Hirota-Satsuma coupled KdV equations arising in shallow water waves

Gupta

Kumar

Singh

2017

Waves, Wavelets and Fractals

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show abstract

“…The fractional KdV equation and the fractional HSKdV are the most important of these type equations [1,21,23]. Firstly, Gardner et al found analytical solution for cKdV, which describes interactions of two long waves with different dispersion relations [6,9], later Hirota and Satsuma introduced a cKdV equation η ϑ − a(η ρρρ + 6ηη ρ ) = 2bϕϕ ρ , (1.1)…”

Section: Introductionmentioning

confidence: 99%

On numerical solutions of time-fraction generalized Hirota Satsuma coupled KdV equation

Aslan¹,

Qurashi²,

Băleanu³

2017

J. Nonlinear Sci. Appl.

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In this study, we obtain the approximate soliton solution of the fractional generalized Hirota-Satsuma coupled Kortewegde Vries equation (GHS-cKdV) within the homotopy analysis method (HAM). Numerical results are successfully compared with other solutions obtained by the differential transform method (DTM) and the homotopy perturbation method (HPM). The numerical results indicate that the only few terms are sufficient to get the correct solutions. Also, the results are given by tables and figures.

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“…Abazari and Abazari [15] have applied DTM There are various design configurations available for solving the generalized Hirota-Satsuma coupled KdV involving different combinations of geometrical details equation. Abbasov et al [16] employed DTM to obtain and airflow patterns.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear Thermal Analysis of Solar Air Heater for the Purpose of Energy Saving

Gorji¹

2012

IJEE

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Abstract:In this article, nonlinear thermal Analysis of air-heating flat-plate solar collectors was conducted to obtain temperature distribution inside the heat transfer unit. Due to temperature-dependency of specific heat coefficient of air, the governing differential equation had a noticeable nonlinear nature. Therefore, for the solution of nonlinear equation a highly accurate and simple analytical method which is called Differential Transformation Method (DTM) and basic numerical method, Runge-Kutta (RG) was employed. As a significant result, it is depicted that the DTM results have an interesting conformity with numerical ones. After this verification, the effects of physical applicable parameters on temperature distribution, useful gained heat and thermal efficiency of collectors were investigated. It was concluded that increase in dimension of collector may not increase the efficiency (about 10% decreased). However an increase in the effectiveness coefficient ( ) and air mass flow rate ( ) enhanced the performance of solar collectors and the process efficiency increased up to 12%.

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Numerical simulation of generalized Hirota–Satsuma coupled KdV equation by RDTM and comparison with DTM

Cited by 68 publications

References 22 publications

An efficient computational approach for generalized Hirota-Satsuma coupled KdV equations arising in shallow water waves

An efficient computational approach for generalized Hirota-Satsuma coupled KdV equations arising in shallow water waves

On numerical solutions of time-fraction generalized Hirota Satsuma coupled KdV equation

Nonlinear Thermal Analysis of Solar Air Heater for the Purpose of Energy Saving

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