Numerical Solution Of Generalized Boussinesq Equation

Firstly, based on high-order compact operators, two kinds of three-layer compact finite difference schemes, which have second-order and fourth-order accuracy in time direction respectively, four-order accuracy in spatial direction, are derived for the linear Boussinesq equation, and the stability conditions of the schemes are given respectively by Fourier analysis method.Secondly, based on average vector field method, a energy-preserving scheme is constructed for the linear "good" Boussinesq equation.Finally, based on multisymplectic theory, the Lagrange function of the nonlinear Boussinesq Paradigm equation is derived, and the Hamiltonian function is obtained by Legendre transformation, then a multi-symplectic systems of the Boussinesq Paradigm equation are deduced through the De Donder-weyl equations. And respectively by Preissmann method and Euler-Box method to discrete the multi-symplectic systems, two kinds of different multi-symplectic schemes are obtained to solve the nonlinear Boussinesq Paradigm equation.The problems such as feasibility and effectiveness of the numerical schemes proposed in this paper are verified by using the MATLAB software.