Numerical study of the Benjamin-Bona-Mahony-Burgers equation

Zarebnia, M.

doi:10.5269/bspm.v35i1.28804

Cited by 12 publications

(7 citation statements)

References 9 publications

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“…Also, the solutions at various times are qualitatively presented in Figure 1. As is the case in the study of Zarebnia and Parvaz [8] and as naturally expected, the amplitude of wave slightly decreases as the time goes on (see Figure 1). x t x t u x t Table 5.…”

Section: Numerical Illustrationsmentioning

confidence: 56%

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A hybrid approach for the regularized long wave-Burgers equation

Zeytinoğlu

Sarı

Allahverdiev

2017

Int. J. Optim. Control, Theor. Appl. (IJOCTA)

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In this paper, a new hybrid approach based on sixth-order finite difference and seventh-order weighted essentially non-oscillatory finite difference scheme is proposed to capture numerical simulation of the regularized long wave-Burgers equation which represents a balance relation among dissipation, dispersion and nonlinearity. The corresponding approach is implemented to the spatial derivatives and then MacCormack method is used for the resulting system. Some test problems discussed by different researchers are considered to apply the suggested method. The produced results are compared with some earlier studies, and to validate the accuracy and efficiency of the method, some error norms are computed. The obtained solutions are in good agreement with the literature. Furthermore, the accuracy of the method is higher than some previous works when some error norms are taken into consideration. Keywords:Regularized

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Section: Numerical Illustrationsmentioning

confidence: 56%

“…The accuracy of the numerical solutions is observed by using absolute error and the following error norms [8]. Also, the solutions at various times are qualitatively presented in Figure 1.…”

Section: Numerical Illustrationsmentioning

confidence: 99%

A hybrid approach for the regularized long wave-Burgers equation

Zeytinoğlu

Sarı

Allahverdiev

2017

Int. J. Optim. Control, Theor. Appl. (IJOCTA)

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“…. The tabulated results have presented for the proposed method and other existing methods [5,11,12,13] in Table 1 [10,14]. , exp sin .…”

Section: Numerical Results and Discussionmentioning

confidence: 99%

Numerical solution of Benjamin-Bona-Mahony-Burger (BBMB) and regularized long-wave (RLW) equations using time-space pseudo-spectral method

Mittal

Balyan

Tiger

2018

J. Phys.: Conf. Ser.

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View the article online for updates and enhancements. Related contentLong-wave instabilities of two interlaced helical vortices H U Quaranta, M Brynjell-Rahkola, T Leweke et al. Abstract. In this research article, an improved numerical scheme is developed for solving the non-linear Benjamin-Bona-Mahony-Burger (BBMB) and regularized long-wave (RLW) equations. The time-space pseudo-spectral method is developed using Chebyshev polynomials at the CGL points. The algebraic mapping is used to transform the initial-boundary value nonhomogeneous problem into the homogeneous problem and further, the BBMB and RLW equations are reduced to a system of nonlinear equations. To demonstrate the performance, the method applied to two model problems and approximate results have been compared with the exact solution and other existing methods. The proposed method succeeds to obtain high order accuracy.

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“…( 1) are studied by different approaches. Numerical solutions of BBMB equation has been studied in [39][40][41][42][43]. Solitary and periodic solution obtained via exp-function method [44,45].…”

Section: Introductionmentioning

confidence: 99%

Evolution Behaviour of Breathers and Lump-N-Solitons (N → ∞) for the (2+1)-Dimensional Benjamin-Bona-Mahony-Burgers Equation

2022

Preprint

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Several types of exact solution of the (2+1)-dimensional Benjamin-Bona-Mahony-Burgers (BBMB) equation will be reported in this research. On the basis of bilinear neural network method (BNNM), some specifific activation functions are precisely taken into the single hidden layer neural nework model, different forms of breather wave solutions, lump solutions and novel hybrid solutions are proposed. By means of symbolic computation and making use of Mathematica software, exact breather wave solutions, lump solutions and lump-N-soliton solutions are constructed completely. The obtained results enrich the knowledge of BBMB equation in the current studies. Various fifigures are plotted to exhibit the interesting evolution characteristic of theses waves vividly. The proposed methods effffectively enable us to understand and investigate the nonlinear evolution equations in plasma physics, oceanography, optical fifibers and flfluid mechanics.

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Numerical study of the Benjamin-Bona-Mahony-Burgers equation

Cited by 12 publications

References 9 publications

A hybrid approach for the regularized long wave-Burgers equation

A hybrid approach for the regularized long wave-Burgers equation

Numerical solution of Benjamin-Bona-Mahony-Burger (BBMB) and regularized long-wave (RLW) equations using time-space pseudo-spectral method

Evolution Behaviour of Breathers and Lump-N-Solitons (N → ∞) for the (2+1)-Dimensional Benjamin-Bona-Mahony-Burgers Equation

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