Abstract
We study the initial-boundary problem of dissipative symmetric regularized long wave equations with damping term by finite difference method. A linear three-level implicit finite difference scheme is designed. Existence and uniqueness of numerical solutions are derived. It is proved that the finite difference scheme is of second-order convergence and unconditionally stable by the discrete energy method. Numerical simulations verify that the method is accurate and efficient.
Highlights
A symmetric version of regularized long wave equation SRLWE, ut ρx uux − uxxt 0, 1.1 ρt ux 0, has been proposed to model the propagation of weakly nonlinear ion acoustic and space charge waves 1
Eliminating ρ from 1.1, we get a class of SRLWE: utt − uxx
The SRLW equation arises in many other areas of mathematical physics 4–6
Summary
A symmetric version of regularized long wave equation SRLWE , ut ρx uux − uxxt 0, 1.1 ρt ux 0, has been proposed to model the propagation of weakly nonlinear ion acoustic and space charge waves 1. In 8 , Guo studied the existence, uniqueness, and regularity of the numerical solutions for the periodic initial value problem of generalized SRLW by the spectral method. It is more significant to study the dissipative symmetric regularized long wave equations with the damping term ut ρx − υuxx uux − uxxt 0, 1.4 ρt ux γ ρ 0, 1.5 where υ, γ are positive constants, υ > 0 is the dissipative coefficient, and γ > 0 is the damping coefficient.
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