In this paper, we consider a generalized BenjaminBona-Mahony-Burgers equation. Classical symmetries of this equation are considered. The functional forms, for which the BBMB equation can be reduced to ordinary differential equations by classical Lie symmetries, are obtained. A catalogue of symmetry reductions and a catalogue of exact solutions are given. A set of new solitons, kinks, antikinks,...

A quadratic B-spline finite element method for the spatial variable combined with a Newton method for the time variable is proposed to approximate a solution of Benjamin-Bona-Mahony-Burgers (BBMB) equation. Two examples were considered to show the efficiency of the proposed scheme. The numerical solutions obtained for various viscosity were compared with the exact solutions. The numerical resul...

In this paper, numerical solutions of the nonlinear Benjamin-Bona-Mahony-Burgers (BBMB) equation are obtained by a method based on collocation of cubic B-splines. Applying the Von-Neumann stability analysis, the proposed method is shown to be unconditionally stable. The method is applied on some test examples, and the numerical results have been compared with the exact solutions. The L∞ and L2 ...

In this work, we implement a relatively new analytical technique, the Exp-Function method, for solving special form of generalized nonlinear Benjamin–Bona–Mahony–Burgers equation (BBMB) which may contain high nonlinear terms. This method can be used as an alternative to obtain analytic and approximate solutions of different types of fractional differential equations applied in engineering mathe...

In this paper, numerical solution of the Benjamin-Bona-Mahony-Burgers (BBMB) equation is obtained by using the mesh-free method based on the collocation method with radial basis functions (RBFs). Stability analysis of the method is discussed. The method is applied to several examples and accuracy of the method is tested in terms of $L_2$ and $L_infty$ error norms.

The paper explores the power of two system­ atic Branch and Bound search algorithms that exploit partition-based heuristics, BBBT (a new algorithm for which the heuristic information is constructed during search and allows dy­ namic variable/value ordering) and its predeces­ sor BBMB (for which the heuristic information is pre-compiled) and compares them against a number of popular local search...

The paper describes a new generic branch and bound scheme that uses heuristics generated mechanically by the mini-bucket approximation. The scheme is presented and evaluated for the Most Probable Explanation (MPE) task in Bayesian networks. We show that the mini-bucket scheme yields monotonic heuristics of varying strengths which cause different amounts of pruning during search. The resulting B...

By means of the idea of three-wave method, we obtain some analytic solutions for high nonlinear form of Benjamin-BonaMahony-Burgers (shortly BBMB) equations in its bilinear form. Keywords—Benjamin-Bona-Mahony-Burgers equations, Hirota’s bilinear form, Three-wave method.

In this paper, we improve b-spline collocation method for Benjamin-Bona-Mahony-Burgers (BBMB) by using defect correction principle. The exact finite difference scheme is used to find defect and the defect correction principle is used to improve collocation method. The method is tested on somemodel problems and the numerical results have been obtained and compared.

In the present manuscript, Benjamin-Bona-Mahony-Burgers (BBMB) equation will be handled numerically by Strang time-splitting technique. While applying this technique, collocation method based on quintic B-spline basis functions is applied. line with our purpose, after splitting BBM-Burgers given appropriate initial boundary conditions into two subequations containing derivative in terms of time...