Methods for the numerical solution of the Benjamin-Bona-Mahony-Burgers equation

DOI10.1002/num.20330zbMath1165.65059OpenAlexW2156771303WikidataQ115398588 ScholiaQ115398588MaRDI QIDQ3539904

Khaled Omrani, Tlili Kadri, Faycal Abidi, Noomen Khiari

Publication date: 19 November 2008

Published in: Numerical Methods for Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/num.20330

zbMATH Keywords

error estimatesfinite element methodweak formulationGalerkin's methodbackward Euler methodquasi-optimal convergenceBenjamin-Bona-Mahony equationregularized long-wave equationfully discrete schemessemidiscrete schemestwo-step backward differentiation methodBenjamin-Bona-Mahony-Burgers (BBMB) equation

Mathematics Subject Classification ID

Navier-Stokes equations (35Q30) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) Method of lines for initial value and initial-boundary value problems involving PDEs (65M20)

Related Items (19)

Numerical solution for Benjamin-Bona-Mahony-Burgers equation with Strang time-splitting technique ⋮ Conservative difference scheme of solitary wave solutions of the generalized regularized long-wave equation ⋮ Convergence and stability in maximum norms of linearized fourth-order conservative compact scheme for Benjamin-Bona-Mahony-Burgers' equation ⋮ An inverse problem for the damped generalized regularized long wave equation ⋮ The numerical analysis of two linearized difference schemes for the <scp>Benjamin–Bona–Mahony–Burgers</scp> equation ⋮ Numerical and theoretical discussions for solving nonlinear generalized Benjamin–Bona–Mahony–Burgers equation based on the Legendre spectral element method ⋮ Two conservative difference schemes for a model of nonlinear dispersive equations ⋮ Analysis and simulation of Korteweg-de Vries-Rosenau-regularised long-wave model via Galerkin finite element method ⋮ Galerkin finite element solution for Benjamin-Bona-Mahony-Burgers equation with cubic B-splines ⋮ An efficient numerical method for solving Benjamin–Bona–Mahony–Burgers equation using difference scheme ⋮ Numerical simulation of the modified regularized long wave equation by split least-squares mixed finite element method ⋮ A high-order linearized difference scheme preserving dissipation property for the 2D Benjamin-Bona-Mahony-Burgers equation ⋮ Numerical solutions for the damped generalized regularized long-wave equation with a variable coefficient by Adomian decomposition method ⋮ Finite element method of BBM-Burgers equation with dissipative term based on adaptive moving mesh ⋮ Analysis and computational method based on quadratic B-spline FEM for the Rosenau-Burgers equation ⋮ Unnamed Item ⋮ Numerical simulation of the modified regularized long wave equation by He's variational iteration method ⋮ Unconditional superconvergence analysis of an energy-stable finite element scheme for nonlinear Benjamin-Bona-Mahony-Burgers equation ⋮ VARIATIONAL PRINCIPLE AND APPROXIMATE SOLUTION FOR THE FRACTAL GENERALIZED BENJAMIN–BONA–MAHONY–BURGERS EQUATION IN FLUID MECHANICS

Cites Work

• Approximate wave solutions for generalized Benjamin-Bona-Mahony-Burgers equations
• The convergence of fully discrete Galerkin approximations for the Benjamin--Bona--Mahony (BBM) equation
• On the convergence of difference schemes for the Benjamin-Bona-Mahony (BBM) equation
• Weak solutions for a nonlinear dispersive equation
• A numerical simulation of solitary-wave solutions of the generalized regularized long-wave equation.
• Finite difference approximate solutions for the two-dimensional Burgers' system.
• Exact and numerical traveling wave solutions for nonlinear coupled equations using symbolic computation
• Error estimates for a Galerkin method for a class of model equations for long waves
• Numerical methods and error analysis for the nonlinear Sivashinsky equation
• Superconvergence of a Finite Element Approximation to the Solution of a Sobolev Equation in a Single Space Variable
• The initial-value problem for the Korteweg-de Vries equation
• Existence and Uniqueness for Periodic Solutions of the Benjamin–Bona–Mahony Equation
• Time-Stepping Galerkin Methods for Nonlinear Sobolev Partial Differential Equations
• Large-time behavior of solution for generalized Benjamin–Bona–Mahony–Burgers equations
• Numerical solution of an evolution equation with a positive-type memory term
• Finite element Galerkin method for the “good” Boussinesq equation
• Model equations for long waves in nonlinear dispersive systems
• Convergence of Galerkin approximations for the Kuramoto‐Tsuzuki equation

This page was built for publication: Methods for the numerical solution of the Benjamin-Bona-Mahony-Burgers equation