A fully Galerkin method for the damped generalized regularized long‐wave (DGRLW) equation

Abstract

In this article, a fully discrete Galerkin scheme based on a nonlinear Crank-Nicolson method to approximate the solution of the DGRLW equation is constructed. Some a priori bounds are proved as well as error estimates. Then, a linearized modification scheme by an extrapolation method is discussed. The two schemes are time second order convergence. The last part is devoted to some numerical results.

Optimal Homotopy Asymptotic Method to Nonlinear Damped Generalized Regularized Long-Wave Equation

“…Yousefi et al used Bernstein Ritz-Galerkin Method for solving the DGRLW equation [6]. Achouri et al worked on an article called "A fully Galerkin method for the damped generalized regularized long-wave (DGRLW) equation, " namely, in [7]. For the mathematical theory and physical significance of DGRLW equation see [8][9][10][11][12][13][14][15][16] and references therein.…”

On the convergence of difference schemes for generalized Benjamin–Bona–Mahony equation

“…Certain numerical methods (Galerkin [4][5][6][7], least squares [8,9], collocation [10][11][12][13], Adomian decomposition [14][15][16], finite differences [17][18][19][20][21][22][23][24][25][26], etc.) are devoted to problems posed for BBM equation and its generalized forms.…”

Numerical simulation of the modified regularized long wave equation by He's variational iteration method

“…Numerical methods of Eqs. (1), (2), and (3) have been proposed by several researchers, based on either finite differences [2][3][4], finite elements [5][6][7][8][9], Adomian decomposition method [10,11], or homotopy perturbation method [12]. The aim of this article is to derive the numerical solution of the MRLW equation using the variational iteration method (shortly VIM).…”