Abstract
We study the initial‐boundary problem of dissipative symmetric regularized long wave equations with damping term. Crank‐Nicolson nonlinear‐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 the theoretical analysis.
Highlights
A symmetric version of regularized long wave equation SRLWE, uxxt − ut ρx uux, 1.1 ρt ux 0, has been proposed to model the propagation of weakly nonlinear ion acoustic and space charge waves 1
We study the initial-boundary problem of dissipative symmetric regularized long wave equations with damping term
Numerical investigation indicates that interactions of solitary waves are inelastic 7 the solitary wave of the SRLWE is not a solution
Summary
A symmetric version of regularized long wave equation SRLWE , uxxt − ut ρx uux, 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. There are other methods such as pseudospectral method, finite difference method for the initial-boundary value problem of SRLWEs see 10–15. Since the form of SRLW equations is similar ro the Rosenau equation and Rosenau-Burgers equation, the established difference schemes in 22, 23 for solving Rosenau equation and Rosenau-Burgers equation are helpful to investigate the SRLWEs. We propose the Crank-Nicolson finite difference scheme for 1.4 – 1.6 which can start by itself. We will show that this difference scheme is uniquely solvable, convergent and stable in both theoretical and numerical senses
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