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

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 partial derivative u/partial derivative t = -v and partial derivative phi/partial derivative t = partial derivative 2 psi/partial derivative x(2) 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(Delta t(2) + h(2)) and O(Delta t(2) + h(4)) in L-infinity- and L-2-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. (C) 2021 IMACS. Published by Elsevier B.V. All rights reserved.

Automated summary

Novel linearized implicit difference schemes with energy conservation property are constructed to simulate the propagation of fractional Klein-Gordon-Zakharov system. The convergence of the constructed algorithms is proven using discrete energy method. Numerical examples demonstrate the effectiveness of the suggested schemes.