The Study On High Order Exponential Integrator Fourier Pseudo–Spectral Methods For The“Good”Boussinesq Equation

In this paper,we propose two kinds of high order exponential integrator Fourier pseudo–spectral methods for solving the nonlinear “Good” Boussinesq(GB)equation.One is a Deuflhard–type k step exponential integrator Fourier pseudo–spectral method(DEI–FPk),which is using Fourier pseudo–spectral method for spatial discretization and using Deuflhard–type exponential integrator for temporal discretization.The other is a Gautschi–type k step exponential integrator Fourier pseudo–spectral method(GEI–FPk),which is using Fourier pseudo–spectral method for spatial discretization and using Gautschi–type exponential integrator for temporal discretization.Two kinds of methods are fully explicit and e cient due to the fast Fourier transform.We also establish rigourous error estimates for two kinds of methods without any Courant–Friedrichs–Lewy(CFL)type condition constraint,that is,they both have k + 1 order accuracy in time and spectral accuracy in space.Extensive numerical experiments are reported to confirm the theoretical analysis and demonstrate rich dynamics of the GB equation,such as birth of solitons and interaction of two solitons,etc.