A new four stages symmetric two-step method with vanished phase-lag and its first derivative for the numerical integration of the Schrödinger equation

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• 作者：Minjian Liang ; T. E. Simos
• 关键词：Phase ; lag ; Derivative of the phase ; lag ; Symmetric ; Hybrid ; Multistep ; Schrödinger equation
• 刊名：Journal of Mathematical Chemistry
• 出版年：2016
• 出版时间：May 2016
• 年：2016
• 卷：54
• 期：5
• 页码：1187-1211
• 全文大小：825 KB
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• 作者单位：Minjian Liang (1) (2)
  T. E. Simos (3) (4) (5)
  
  1. School of Information Engineering, Changan University, Xi’an, 710064, People’s Republic of China
  2. Guangdong Special Equipment Inspection and Research Institute Branch of Zhuhai, Zhuhai, 519002, People’s Republic of China
  3. Department of Mathematics, College of Sciences, King Saud University, P. O. Box 2455, Riyadh, 11451, Saudi Arabia
  4. Laboratory of Computational Sciences, Department of Informatics and Telecommunications, Faculty of Economy, Management and Informatics, University of Peloponnese, 221 00, Tripolis, Greece
  5. 10 Konitsis Street, Amfithea - Paleon Faliron, 175 64, Athens, Greece
  
• 刊物类别：Chemistry and Materials Science
• 刊物主题：Chemistry
  Physical Chemistry
  Theoretical and Computational Chemistry
  Mathematical Applications in Chemistry
  
• 出版者：Springer Netherlands
• ISSN：1572-8897

文摘

In this paper a four stages symmetric two-step method with vanished phase-lag and its first derivative with high algebraic order is developed for the first time in the literature. More pricesly in this paper the following are presented: (1) the phase-lag analysis for the construction of the new high algebraic order method, (2) the construction of the new method, (3) the error analysis based on the radial Schrödinger equation, (4) the interval of periodicity analysis and the stability analysis, (5) a new error estimation procedure based on the phase-lag (6) the numerical tests for the study of the efficiency of the new obtained method which are based on the numerical solution of the Schrödinger equation.