Explicit two-step high-accuracy hybrid methods with minimal phase-lag for y″ = f(x, y) and their application to the one-dimensional Schrödinger equation

✍ Scribed by Kaili Xiang; Jianjun Zhang

• Book ID: 104338676
• Publisher: Elsevier Science
• Year: 1998
• Tongue: English
• Weight: 471 KB
• Volume: 95
• Category: Article
• ISSN: 0377-0427
• DOI: 10.1016/s0377-0427(98)00051-x

✦ Synopsis

In this paper, two families of explicit two-step sixth and eighth algebraic order hybrid methods with minimal phaselag are developed for the numerical integration of special second-order periodic initial-value problems. These methods have the advantage of higher algebraic accuracy and minimal phase-lag compared with some methods in [1,2,[4][5][6][7][8][11][12][13][14]. The methods proposed in this paper may be considered as a generalization of some methods in [1,5,7,8,12]. An application to the one-dimensional Schrodinger equation on the resonance problem indicates that these new methods are generally more accurate than some methods in [5-8, 2, 11, 13, 14]. (~) 1998 Elsevier Science B.V. All rights reserved.