A conservative splitting difference scheme for the fractional-in-space Boussinesq equation

Abstract

In this paper, an efficient energy-preserving splitting Crank-Nicolson difference scheme for the fractional-in-space Boussinesq equation is established. The novelty of the proposed scheme here is that the potential function v is introduced via ∂u∂t=−(−Δ)α2v to ensure the conservation of energy. By utilizing the discrete energy method, it is shown that the proposed scheme attains the convergence rates of O(Δt2+h2) in the discrete L∞-norm without any restrictions on the grid ratio, and is unconditionally stable. Finally, a linearized iterative algorithm is proposed and numerical results are provided to demonstrate the correctness of the theoretical results.