Efficient high-order structure-preserving methods for the generalized Rosenau-type equation with power law nonlinearity

Based on the multi-symplectic Hamiltonian formula of the generalized Rosenau-type equation, a multi-symplectic scheme and an energy-preserving scheme are proposed. To improve the accuracy of the solution, we apply the composition technique to the obtained schemes to develop high-order schemes which are also multi-symplectic and energy-preserving respectively. Discrete fast Fourier transform makes a significant improvement to the computational efficiency of schemes. Numerical results verify that all the proposed schemes have satisfactory performance in providing accurate solution and preserving the discrete mass and energy invariants. Numerical results also show that although each basic time step is divided into several composition steps, the computational efficiency of the composition schemes is much higher than that of the non-composite schemes.