A fourth-order difference scheme for the fractional nonlinear Schrödinger equation with wave operator. Issue 8 (24th May 2022)

• Record Type: Journal Article
• Authors: Pan, Kejia; Zeng, Jiali; He, Dongdong; Zhang, Saiyan
• Is Part Of: Applicable analysis. Volume 101:Issue 8(2022)
• Page Start: 2886
• Page End: 2902
• Publication Date: 2022-05-24
• Subjects: Nonlinear Schrödinger equation -- fractional Laplacian -- wave operator -- unconditional stability -- semi-implicit difference scheme; 65M06; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2020.1829600
• Languages: English
• ISSNs: 0003-6811

Abstract

ABSTRACT: In this paper, an efficient semi-implicit difference scheme for solving the fractional nonlinear Schrödinger equation with wave operator are proposed and analyzed. The semi-implicit scheme involves three-time levels, is unconditionally stable and fourth-order accurate in space and second-order accurate in time. Furthermore, the unique solvability, unconditional stability and convergence of the method in the L ∞ -norm are proved rigorously by the energy method. Finally, numerical experiments are presented to confirm our theoretical results.