Conservative finite difference methods for fractional Schrödinger–Boussinesq equations and convergence analysis. Issue 4 (13th January 2019)

• Record Type: Journal Article
• Authors: Liao, Feng; Zhang, Luming; Hu, Xiuling
• Is Part Of: Numerical methods for partial differential equations. Volume 35:Issue 4(2019)
• Page Start: 1305
• Page End: 1325
• Publication Date: 2019-01-13
• Subjects: conservative law -- convergence -- discrete energy method -- mathematical induction method -- Schrödinger–Boussinesq equations; Differential equations, Partial -- Numerical solutions -- Periodicals; 515.353
• DOI: 10.1002/num.22351
• Languages: English
• ISSNs: 0749-159X

Abstract

Abstract : In this paper, two conservative finite difference schemes for fractional Schrödinger–Boussinesq equations are formulated and investigated. The convergence of the nonlinear fully implicit scheme is established via discrete energy method, while the linear semi‐implicit scheme is analyzed by means of mathematical induction method. Our schemes are proved to preserve the total mass and energy in discrete level. The numerical results are given to confirm the theoretical analysis.