A conservative difference scheme for two‐dimensional nonlinear Schrödinger equation with wave operator. Issue 3 (30th December 2015)

• Record Type: Journal Article
• Authors: Hu, Hanzhang; Chen, Yanping
• Is Part Of: Numerical methods for partial differential equations. Volume 32:Issue 3(2016:May)
• Page Start: 862
• Page End: 876
• Publication Date: 2015-12-30
• Subjects: Schrödinger equation -- difference scheme -- conservative -- convergence -- stability -- energy estimate; Differential equations, Partial -- Numerical solutions -- Periodicals; 515.353
• DOI: 10.1002/num.22033
• Languages: English
• ISSNs: 0749-159X

Abstract

Abstract : A conservative difference scheme is presented for two‐dimensional nonlinear Schrödinger equation with wave operator. The discrete energy method and an useful technique are used to analyze the difference scheme. It is shown, both theoretically and numerically, that the difference solution is conservative, unconditionally stable and convergent with second order in maximum norm. A numerical experiment indicates that the scheme is very effective. © 2015 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 32: 862–876, 2016