An explicit structure-preserving algorithm for the nonlinear fractional Hamiltonian wave equation. (April 2020)

• Record Type: Journal Article
• Authors: Fu, Yayun; Cai, Wenjun; Wang, Yushun
• Is Part Of: Applied mathematics letters. Volume 102(2020)
• Publication Date: 2020-04
• Subjects: Nonlinear fractional wave equation -- Hamiltonian system -- Explicit energy-preserving scheme -- Fourth-order difference formula; Applied mathematics -- Periodicals; 519.05
• DOI: 10.1016/j.aml.2019.106123
• Languages: English
• ISSNs: 0893-9659

Abstract

Abstract: In this paper, we propose a new approach to construct an explicit structure-preserving scheme for the nonlinear fractional wave equation. First, we reformulate the equation as a canonical Hamiltonian system. Then, we utilize the fourth-order fractional centered difference formula to discretize the equation in space direction, and obtain a conservative semi-discrete system. Subsequently, we develop an explicit fully-discrete energy-preserving scheme for the equation by using the proposed approach. Numerical examples are provided to confirm our theoretical analysis in long time computations at last.