scholarly journals A Galerkin Finite Element Method for Numerical Solutions of the Modified Regularized Long Wave Equation

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Liquan Mei ◽  
Yali Gao ◽  
Zhangxin Chen
Keyword(s):  
Wave Equation ◽  
Theoretical Study ◽  
Numerical Solutions ◽  
Galerkin Finite Element Method ◽  
Galerkin Finite Element ◽  
Long Wave ◽  
Regularized Long Wave Equation ◽  
Time Accuracy ◽  
Nicolson Scheme ◽  
Invariants Of Motion

A Galerkin method for a modified regularized long wave equation is studied using finite elements in space, the Crank-Nicolson scheme, and the Runge-Kutta scheme in time. In addition, an extrapolation technique is used to transform a nonlinear system into a linear system in order to improve the time accuracy of this method. A Fourier stability analysis for the method is shown to be marginally stable. Three invariants of motion are investigated. Numerical experiments are presented to check the theoretical study of this method.

Novel Transparent Boundary Conditions for the Regularized Long Wave Equation

2019 ◽  
Vol 17 (06) ◽  
pp. 1950021
Author(s):  
M. Abounouh ◽  
H. Al-Moatassime ◽  
S. Kaouri
Keyword(s):  
Wave Equation ◽  
Initial Data ◽  
Boundary Conditions ◽  
Transparent Boundary Conditions ◽  
Long Wave ◽  
Regularized Long Wave Equation ◽  
Space Discretization ◽  
Infinite Norm ◽  
Nicolson Scheme ◽  
Norm Error

In this paper, we present a new method to derive transparent boundary conditions for the Regularized Long Wave equation and its linearized equation. These boundary conditions have the advantage of being exact for both linearized and nonlinear equations. The resulting problems supplemented with initial data are approximated numerically using finite difference method in space discretization and Crank–Nicolson scheme in time for the linearized equation, while implicit scheme in time is used for the Regularized Long Wave equation. Numerical experiments are made for solitary initial data and various source terms to illustrate the transparency of the introduced boundary conditions. Results are compared with the use of usual boundary conditions, namely, Dirichlet and Neumann via infinite norm error on the boundary and also by displaying geophones and instantaneous figures.

scholarly journals A linear finite difference scheme for the generalized dissipative symetric regularized long wave equation with damping

2019 ◽  
Vol 23 (Suppl. 3) ◽  
pp. 719-726 ◽  
Author(s):  
Xi Wang ◽  
Jin-Song Hu ◽  
Hong Zhang
Keyword(s):  
Wave Equation ◽  
Finite Difference ◽  
Difference Scheme ◽  
Finite Difference Scheme ◽  
Numerical Solutions ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Long Wave ◽  
Regularized Long Wave Equation ◽  
Initial Boundary Value

In this paper, we study and analyze a three-level linear finite difference scheme for the initial boundary value problem of the symmetric regularized long wave equation with damping. The proposed scheme has the second accuracy both for the spatial and temporal discretization. The convergence and stability of the numerical solutions are proved by the mathematical induction and the discrete functional analysis. Numerical results are given to verify the accuracy and the efficiency of proposed algorithm.

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