Conservation laws for a family of Benjamin-Bona-Mahony-Burgers equations

Bruzón, M. S.; Gandarias, M. L.

doi:10.1109/nsc.2012.6304747

Cited by 4 publications

(3 citation statements)

References 16 publications

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“…In [22] the traveling wave solutions of the BBM-Burgers equation were obtained by using the ( G G )-expansion method. The Lie classical symmetries and conservative laws for a family of the BBM-Burgers equation were derived in [23]. Bell-shaped and kink-shaped solutions of the generalized BBM-Burgers were found by the improved system technique [24].…”

Section: Introductionmentioning

confidence: 99%

Novel advances in high-order numerical algorithm for evaluation of the shallow water wave equations

Poochinapan

Wongsaijai

2023

Adv Cont Discr Mod

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In this paper, we propose a high-order nonlinear algorithm based on a finite difference method modification to the regularized long wave equation and the Benjamin–Bona–Mahony–Burgers equation subject to the homogeneous boundary. The consequence system of nonlinear equations typically trades with high computation burden. This dilemma can be overcome by establishing a fast numerical algorithm procedure without a reduction of numerical accuracy. The proposed algorithm forms a linear system with constant coefficient matrix at each time step and produces numerical solutions, which remarkably gains many computational advantages. In terms of analysis, a priori estimation for the numerical solution is derived to obtain the convergence and stability analysis. Additionally, the algorithm is globally mass preserving to avoid nonphysical behavior. Two benchmarks, including a single solitary wave to both equations, are given to validate the applicability and accuracy of the proposed method. Numerical results are obtained and compared to other approaches available in the literature. From the comparisons it is clear that the proposed approach produces accurate and precise results at low computational cost. Besides, the proposed scheme is applied to study the effect of the viscous term on a single solitary wave. It is shown that the viscous term results in the amplitude and width of the initial condition but not in its velocities in the case of a single solitary wave. As a consequence, theoretical and numerical findings provide a new area to investigate and expand the high-order algorithm for the family of wave equations.

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Section: Introductionmentioning

confidence: 99%

Novel advances in high-order numerical algorithm for evaluation of the shallow water wave equations

Poochinapan

Wongsaijai

2023

Adv Cont Discr Mod

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“…For the work on exact solution and conservation laws of BBMB equation, we refer to [8][9][10]. Peregrine [11] proposed the regularized long wave (RLW) equation (a particular case of GRLW with p = 1 in (4)) along with a finite difference method to study undular bore.…”

Section: Introductionmentioning

confidence: 99%

B-spline quasi-interpolation based numerical methods for some Sobolev type equations

Kumar

Baskar

2016

Journal of Computational and Applied Mathematics

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a b s t r a c tIn this article, we intend to use quadratic and cubic B-spline quasi-interpolants to develop higher order numerical methods for some Sobolev type equations in one space dimension. Our aim is also to compare the performance of the proposed methods in terms of the accuracy and the rate of convergence. We also discuss another approach to the cubic B-spline quasi-interpolation based method, where we achieve fourth order of accuracy in space. We theoretically establish the order of accuracy for the three proposed methods and also establish the L 2 -stability in the linear case using von Neumann analysis. As a particular case of the Sobolev type equations, we take the equal width and the Benjamin-Bona-Mahony-Burgers equations, and perform several numerical experiments to support our theoretical results.

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“…Lie symmetries, in general, symmetry groups, have several applications in the context of nonlinear differential equations. It is noteworthy that they are used to obtain exact solutions and conservation laws of partial differential equations [5,6,7,16,22].…”

Section: Introductionmentioning

confidence: 99%

On symmetries and conservation laws of a Gardner equation involving arbitrary functions

Rosa

Gandarias

Bruzón

2016

Applied Mathematics and Computation

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Conservation laws for a family of Benjamin-Bona-Mahony-Burgers equations

Cited by 4 publications

References 16 publications

Novel advances in high-order numerical algorithm for evaluation of the shallow water wave equations

Novel advances in high-order numerical algorithm for evaluation of the shallow water wave equations

B-spline quasi-interpolation based numerical methods for some Sobolev type equations

On symmetries and conservation laws of a Gardner equation involving arbitrary functions

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