A new efficient energy-preserving finite volume element scheme for the improved Boussinesq equation

摘要

In this paper, a new linearized energy-preserving Crank-Nicolson finite volume element scheme is derived for the improved Boussinesq equation. The fully discrete scheme can be shown to conserve both mass and energy in the discrete setting. It is proved that the scheme is uniquely solvable and convergent with the rate of order two in a discrete L_2 norm. At last, a series of numerical experiments on typical improved Boussinesq and Sine-Gordon equations are provided to verify our theoretical results and to show the efficiency and accuracy of the proposed scheme.