Hermite pesudospectral method and modified Hermite spectral method for long-short wave equations

We consider the initial boundary value problem of the long-short wave equations on the whole line.Firstly, a fully discrete Hermite pseudospectral scheme and modified Hermite spectral scheme are structured basing Hermite functions, respectively.Secondly, we analyze the two kinds of schemes theoretically.The modified Hermite spectral scheme shows the superiority in priori estimates, numerical stability and convergence.Thirdly, numerical experiments for the two schemes are presented to confirm our theoretical analysis.