Linear implicit finite difference methods with energy conservation property for space fractional Klein-Gordon-Zakharov system

Abstract

In this article, novel linearized implicit difference schemes with energy conservation property for fractional Klein-Gordon-Zakharov system are constructed and analyzed. The important feature of the article is that new auxiliary equations ∂u∂t=−v and ∂ϕ∂t=∂2ψ∂x2 are introduced to transform the original fractional Klein-Gordon-Zakharov system into an equivalent system of equations exactly. Especially, two kinds of efficacious difference operators, the leap-frog and modified Crank-Nicolson methods are respectively utilized to establish the linearized implicit difference schemes with energy conservation property for simulating the propagation of transformed equations. And above all, by employing the discrete energy method, we have proven that the constructed difference algorithms enjoy the convergence order of O(Δt2+h2) and O(Δt2+h4) in L∞- and L2-norms, without imposing any restrictive conditions on the grid ratio compared with the existing literature. Two numerical examples are carried out to investigate the physical behaviors of the wave propagation and substantiate the effectiveness of the suggested schemes.