Quadratic B-Spline Finite Element Method for the Benjamin-Bona-Mahony-Burgers Equation

Yin, Y; Piao, Guang-Ri

doi:10.7858/eamj.2013.034

Cited by 5 publications

(3 citation statements)

References 15 publications

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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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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

View full text Add to dashboard Cite

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“…The moving mesh method is a kind of adaptive mesh method which adds elements near the place where the numerical solution changes rapidly and decreases elements in the solution changing slowly; the total element number still remains unchanged. When we compare the finite element method based on adaptive moving mesh with methods based on fixed mesh or proposed in [26], we find that the moving mesh method takes fewer elements to get the same distinguishability and simulates steep waves and the transition of gap distinctly. In recent years, the moving mesh method has witnessed further development and extensive application [35].…”

Section: Introductionmentioning

confidence: 99%

“…Ganji et al put forward the notion that the method they used in [22] is better than the homotopy analysis method proposed in [23]. Finite element Galerkin methods have been discussed by Kadri et al [24], Lee [25], Yin and Piao [26], and Dehghan et al [27] to solve the BBM-Burgers equations with a dissipative term. Finite difference methods have also been widely used to solve the equations in [28][29][30]; as for other numerical methods, refer to [31][32][33][34].…”

Section: Introductionmentioning

confidence: 99%

Finite Element Method of BBM-Burgers Equation with Dissipative Term Based on Adaptive Moving Mesh

Gao

et al. 2017

Discrete Dynamics in Nature and Society

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A finite element model is proposed for the Benjamin-Bona-Mahony-Burgers (BBM-Burgers) equation with a high-order dissipative term; the scheme is based on adaptive moving meshes. The model can be applied to the equations with spatial-time mixed derivatives and high-order derivative terms. In this scheme, new variables are needed to make the equation become a coupled system, and then the linear finite element method is used to discretize the spatial derivative and the fifth-order Radau IIA method is used to discretize the time derivative. The simulations of 1D and 2D BBM-Burgers equations with high-order dissipative terms are presented in numerical examples. The numerical results show that the method keeps a second-order convergence in space and provides a smaller error than that based on the fixed mesh, which demonstrates the effectiveness and feasibility of the finite element method based on the moving mesh. We also study the effect of the dissipative terms with different coefficients in the equation; by numerical simulations, we find that the dissipative term plays a more important role than in dissipation.

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Galerkin finite element solution for Benjamin–Bona–Mahony–Burgers equation with cubic B-splines

Karakoç

Bhowmik

2019

Computers & Mathematics with Applications

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Quadratic B-Spline Finite Element Method for the Benjamin-Bona-Mahony-Burgers Equation

Cited by 5 publications

References 15 publications

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

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

Finite Element Method of BBM-Burgers Equation with Dissipative Term Based on Adaptive Moving Mesh

Galerkin finite element solution for Benjamin–Bona–Mahony–Burgers equation with cubic B-splines

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