A Conservative Finite Difference Reaserch For Dissipative Symmetric Regularized Long Wave Equation

On the research of the spread of the weakly nonlinear ion acoustic wave and the space with waves, theprinciple of dissipation must be taken into consideration for the resistance of propagation medium and thefriction between the air need to be overcame. Therefore, the generalized symmetric regularized long waveequation with dissipation term is the rational model to reflect the essence of the phenomenon of nonlinear ionacoustic wave motion. In this paper,a finite difference method is proposed for the initial valueproblems of dissipative symmetric regularized long wave equation was presented. Under thepremise of keeping the second-order accuracy, a conservative implicit unfinite difference of twolevels with weight coefficient and an energy conservative implicit weighted finite difference ofthree levels on the space were proposed by LAX scheme，and then an energy conservativethree levels finite difference with weight coefficient on the time was proposed.Those schemesimulates two conservation properties of the problem well.Error estimates based on energymethods are derived.Existence and uniqueness of numerical solutions were derived,It is provedthat the finite difference scheme is convergent in orderO (τ2+h2)and stable.The results attainedform numerical experiments show that the method is reliable and efficient.