Finite Difference Approximation For Generalized SRLWE With Damping Term

In applications, the viscous damping effect is inevitable and it plays the same importantrole as the dispersive effect. For the influence of damping and dissipation, generalized SRLWEare a reasonable model to render essential phenomena of nonlinear ion acoustic wave motionwhen dissipation is considered, and it is meaningful to research of its numerical solution. In thispaper, a finite difference method for the damping dissipative generalized SRLWE with ahomogeneous boundary conditions was considered. Both a nonlinear two-level conservativefinite difference scheme and a linear three-level conservative finite difference scheme aredesigned. The nonlinear two-level conservative finite difference scheme simulate theconservation properties of the problem well. It is shown that the priori error estimate anduniquely solvable for the solutions of those finite difference schemes. It is proved that thosefinite difference schemes was a convergence of second-order convergence and unconditionallystable by the discrete energy method. Numerical examples confirm the theoretical results.