Abstract
The generalized regularized long-wave (GRLW) equation is studied by finite difference method. A new fourth-order energy conservative compact finite difference scheme was proposed. It is proved by the discrete energy method that the compact scheme is solvable, the convergence and stability of the difference schemes are obtained, and its numerical convergence order isO(τ2+h4)in theL∞-norm. Further, the compact schemes are conservative. Numerical experiment results show that the theory is accurate and the method is efficient and reliable.
Highlights
In this paper, we consider the following generalized regularized long-wave equation: ut + ux + αx − βuxxt = 0, (x, t) ∈ × (0, T], (1)with the boundary conditions u = u = 0, t ∈ (0, T], (2)and the initial condition u (x, 0) = u0 (x), x ∈, (3)where u = u(x, t) is a real-valued function defined on ×
The generalized regularized long-wave (GRLW) equation can describe that wave motion to the same order of approximation as the KDV equation, so it plays a major role in the study of nonlinear dispersive waves [3]
We aim to present a conservative finite difference scheme for problem (1)–(3), which simulates conservation law (5) that the differential equation (1) possesses, and prove convergence and stability of the scheme
Summary
We consider the following generalized regularized long-wave equation: ut + ux + α (up)x − βuxxt = 0, (x, t) ∈ (xl, xr) × (0, T] , (1). In [14], a time-linearization method that uses a Crank-Nicolson procedure in time and three-point, fourth-order accurate in space, compact difference equations, is presented and used to determine the solutions of the generalized regularized-long wave (GRLW) equation.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
