Approximate analytical solution to fractional modified KdV equations

Abdul-Aziz, O. I.; Hashim, Ishak; Ismail, Eddie Shahril

doi:10.1016/j.mcm.2008.01.005

Cited by 47 publications

(40 citation statements)

References 22 publications

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“…We developed our method for solving this two-dimensional KdV problem. We chose the centers of RBFs (and the collocation points) as ( Table 9 depicts the errors and the experimental convergence orders resulted by our method with M 1 = M 2 = 9 for four different time steps and [a 1 , 1]. In these cases, we got ρ(J G (X * )) < 0.48.…”

Section: Examplementioning

confidence: 99%

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A high order method for numerical solution of time-fractional KdV equation by radial basis functions

Sepehrian

Shamohammadi

2018

Arab. J. Math.

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A radial basis function method for solving time-fractional KdV equation is presented. The Caputo derivative is approximated by the high order formulas introduced in Buhman (Proc. Edinb. Math. Soc. 36:319-333, 1993). By choosing the centers of radial basis functions as collocation points, in each time step a nonlinear system of algebraic equations is obtained. A fixed point predictor-corrector method for solving the system is introduced. The efficiency and accuracy of our method are demonstrated through several illustrative examples. By the examples, the experimental convergence order is approximately 4 − α, where α is the order of time derivative.Mathematics Subject Classification 65D05 · 65M06 · 65N06 · 65N35

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Section: Examplementioning

confidence: 99%

“…A numerical technique based on generalized Taylor series formula has been presented in [13]. For more information, for example, see [1,18,28,33,35].…”

Section: Introductionmentioning

confidence: 99%

A high order method for numerical solution of time-fractional KdV equation by radial basis functions

Sepehrian

Shamohammadi

2018

Arab. J. Math.

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“…[6]. There are many analytic and approximate solution methods proposed to solve fractional mKdV-ZK equation and Maccari system [2,13,15,17,8].…”

Section: Introductionmentioning

confidence: 99%

Functional Variable Method for conformable fractional modified KdV-ZK equation and Maccari system

2017

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Modeling the motion and propagation characteristics of waves have importance in coastal, ocean and maritime engineering. Especially, waves are the major source of environmental actions on beaches or on man-made fixed or floating structures in most geographical areas. So Maccari system has great application in mentioned areas. The modified KdV is ion acoustic perturbations evolution model in a plasma with two negative ion components which have different temperatures. As for the KdV equation, the modified ZK (mZK) equation arises naturally as weakly two-dimensional variations of the mKdV equation. In this paper authors used functional variable method(FVM) for the first time to obtain exact travelling wave and soliton solutions of conformable fractional modified KdV-Zakharov-Kuznetsov(mKdv-ZK) equation and Maccari system. As a consequence, new solutions are obtained and it is seen that FVM is an valuable and efficient tool for solving nonlinear equations and systems where the derivatives defined by means of conformable fractional derivative.

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“…So far, various methods are used for solving different types of fractional KdV equations. These methods can be listed as Adomian decomposition method [1,2], variational iteration method [2], homotopy perturbation method [3][4][5][6][7], differential transform method [8], modified direct algebraic method [9], (G ′ /G) -expansion method [10], improved (G ′ /G) -expansion method [10], homotopy perturbation transform method [11], function expansion method [12]. In this study, we consider the space fractional Korteweg-de Vries equation…”

Section: Introductionmentioning

confidence: 99%

New analytical solutions of the space fractional KdV equation in terms of Jacobi elliptic functions

Daşçıoğlu¹,

Çulha²,

Bayram³

2017

ntmsci

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Abstract:In this study, new families of analytical exact solutions of the space fractional Korteweg-de Vries (KdV) equation are presented. Here, the fractional derivative is considered in conformable sense. By utilizing the Jacobi elliptic function expansion method, the solutions are obtained in general form containing the hyperbolic, trigonometric, and rational functions. Also, the complex valued solutions are obtained and some solutions of this equation are demonstrated.

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Approximate analytical solution to fractional modified KdV equations

Cited by 47 publications

References 22 publications

A high order method for numerical solution of time-fractional KdV equation by radial basis functions

A high order method for numerical solution of time-fractional KdV equation by radial basis functions

Functional Variable Method for conformable fractional modified KdV-ZK equation and Maccari system

New analytical solutions of the space fractional KdV equation in terms of Jacobi elliptic functions

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