Compact and efficient conservative schemes for coupled nonlinear Schrödinger equations. Issue 6 (20th February 2015)

• Record Type: Journal Article
• Authors: Kong, Linghua; Hong, Jialin; Ji, Lihai; Zhu, Pengfei
• Is Part Of: Numerical methods for partial differential equations. Volume 31:Issue 6(2015)
• Page Start: 1814
• Page End: 1843
• Publication Date: 2015-02-20
• Subjects: Differential equations, Partial -- Numerical solutions -- Periodicals; 515.353
• DOI: 10.1002/num.21969
• Languages: English
• ISSNs: 0749-159X

Abstract

<abstract abstract-type="main"> <title> <x xml:space="preserve">Abstract</x> </title> <p>In the manuscript, we present several numerical schemes to approximate the coupled nonlinear Schrödinger equations. Three of them are high‐order compact and conservative, and the other two are noncompact but conservative. After some numerical analysis, we can find that the schemes are uniquely solvable and convergent. All of them are conservative and stable. By calculating the complexity, we can find that the compact schemes have the same computational cost with the noncompact ones. Numerical illustrations support our analysis. They verify that compact schemes are more efficient than noncompact ones from computation cost and accuracy. © 2015 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 31: 1814–1843, 2015</p> </abstract>