Application of variational iteration method for modified Camassa‐Holm and Degasperis‐Procesi equations

Jafari, Hossein; Zabihi, Mehdi; Salehpoor, Elham

doi:10.1002/num.20472

Cited by 7 publications

(5 citation statements)

References 17 publications

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“…The considered equations are analysed and also find the solution via numerical and analytical schemes by many researchers. For instance, authors in [45] find the numerical solution for these equations with the help of variational iteration scheme, homotopy perturbation algorithm is employed [33] and find the solution and presented some interesting consequences, researchers in [46] hired homotopy perturbation technique to analyse the projected equations within the frame of FC and others.…”

Section: Introductionmentioning

confidence: 99%

Novel approach for modified forms of Camassa–Holm and Degasperis–Procesi equations using fractional operator

Veeresha

Prakasha

2020

Commun. Theor. Phys.

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In the present study, we consider the q-homotopy analysis transform method to find the solution for modified Camassa–Holm and Degasperis–Procesi equations using the Caputo fractional operator. Both the considered equations are nonlinear and exemplify shallow water behaviour. We present the solution procedure for the fractional operator and the projected solution procedure gives a rapidly convergent series solution. The solution behaviour is demonstrated as compared with the exact solution and the response is plotted in 2D plots for a diverse fractional-order achieved by the Caputo derivative to show the importance of incorporating the generalised concept. The accuracy of the considered method is illustrated with available results in the numerical simulation. The convergence providence of the achieved solution is established in -curves for a distinct arbitrary order. Moreover, some simulations and the important nature of the considered model, with the help of obtained results, shows the efficiency of the considered fractional operator and algorithm, while examining the nonlinear equations describing real-world problems.

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Section: Introductionmentioning

confidence: 99%

Novel approach for modified forms of Camassa–Holm and Degasperis–Procesi equations using fractional operator

Veeresha

Prakasha

2020

Commun. Theor. Phys.

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“…The CH equation, being a model equation for water waves, has its integrable bi-Hamiltonian structure [5]. In recent years, some works have been done in order to find the numerical solution of this equation, for example [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21]. In this work, we develop the ADM, MADM, VIM, MVIM and HAM to solve the Eq.…”

Section: Introductionmentioning

confidence: 99%

Numerical solution of Hamiltonian model by using homotopy analysis method

Behzadi¹,

Khalilsaray²

2015

Advanced Computational Techniques in Electromagnetics

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In this paper, a Hamiltonian model is solved by using the Adomian's deomposition method (ADM), modified Adomian's decomposition method (MADM), variational iteration method (VIM), modified variation alliteration method (MVIM) and homotopy analysis method (HAM). The approximate solution of this equation is calculated in the form of series which its components are computed by applying a recursive relation. The existence and uniqueness of the solution and the convergence of the proposed methods are proved. A numerical example is studied to demonstrate the accuracy of the presented methods.

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“…The method was first initiated by [6], and it was successfully used by various researchers to investigate the linear and nonlinear problems [6,10]. We mention that Jafari et.al.…”

Section: Introductionmentioning

confidence: 99%

“…We mention that Jafari et.al. applied the variational iteration method to the modified Camassa-Holm and Degasperis-Procesi equations and fractional Davey-Stewartson equations, [9,10]. Momani and Odibat [17] has implemented the variational iteration method to solve nonlinear fractional differential equations.…”

Section: Introductionmentioning

confidence: 99%

A modified variational iteration method for solving fractional Riccati differential equation by Adomian polynomials

Jafari

Tajadodi

Băleanu

2013

fcaa

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In this paper, we introduce a modified variational iteration method (MVIM) for solving Riccati differential equations. Also the fractional Riccati differential equation is solved by variational iteration method with considering Adomians polynomials for nonlinear terms. The main advantage of the MVIM is that it can enlarge the convergence region of iterative approximate solutions. Hence, the solutions obtained using the MVIM give good approximations for a larger interval. The numerical results show that the method is simple and effective.MSC 2010 : Primary 34A08; Secondary 34K28, 34K37

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Application of variational iteration method for modified Camassa‐Holm and Degasperis‐Procesi equations

Cited by 7 publications

References 17 publications

Novel approach for modified forms of Camassa–Holm and Degasperis–Procesi equations using fractional operator

Novel approach for modified forms of Camassa–Holm and Degasperis–Procesi equations using fractional operator

Numerical solution of Hamiltonian model by using homotopy analysis method

A modified variational iteration method for solving fractional Riccati differential equation by Adomian polynomials

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