Two Extrapolation Linearized Difference Algorithms For GSRLW Equation With Damping Term

During the actual propagation of nonlinear waves,viscous damping is inevitable.Due to the consideration of the effects of damping and dissipation,the symmetric regular long-wave equation with damping terms is a reasonable model reflecting the essential phenomenon of nonlinear ion acoustic wave motion.This paper considers a finite difference method for a class of GSRLW equations with damping terms with homogeneous boundary conditions,under the premise of ensuring the second-order theoretical accuracy,when the value is discrete,extrapolate the nonlinear term to the known layer(n-1 layer)of the difference format by two methods,thus,two new linear extrapolation time difference schemes are proposed,and the existence and uniqueness of the solutions are proved.In the case where the maximum modulus prior estimate of the difference decomposition cannot be obtained,Comprehensive use of mathematical induction and discrete functional analysis methods directly proves the convergence and stability of these two formats.Numerical examples show that both linear difference formats are valid.