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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 910624, 11 pages
http://dx.doi.org/10.1155/2013/910624
Research Article

The Use of Phase Lag and Amplification Error Derivatives for the Construction of a Modified Runge-Kutta-Nyström Method

1Department of Business Administration, Faculty of Management and Economy, Technological Educational Institute of Patras, 26 334 Patras, Greece
2Department of Mathematics, College of Sciences, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia
3Laboratory of Computational Sciences, Department of Computer Science and Technology, Faculty of Sciences and Technology, University of Peloponnese, 22 100 Tripolis, Greece

Received 14 November 2012; Revised 16 March 2013; Accepted 3 April 2013

Academic Editor: Juan Carlos Cortés López

Copyright © 2013 D. F. Papadopoulos and T. E. Simos. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Citations to this Article [26 citations]

The following is the list of published articles that have cited the current article.

  • Ali Shokri, and Hosein Saadat, “Trigonometrically fitted high-order predictor–corrector method with phase-lag of order infinity for the numerical solution of radial Schrödinger equation,” Journal of Mathematical Chemistry, 2014. View at Publisher · View at Google Scholar
  • T. E. Simos, “A new explicit four-step method with vanished phase-lag and its first and second derivatives,” Journal of Mathematical Chemistry, 2014. View at Publisher · View at Google Scholar
  • Fei Hui, and T. E. Simos, “A new family of two stage symmetric two-step methods with vanished phase-lag and its derivatives for the numerical integration of the Schrödinger equation,” Journal of Mathematical Chemistry, 2015. View at Publisher · View at Google Scholar
  • Yanping Yang, Ke Wu, and Yonglei Fang, “Exponentially fitted TDRK pairs for the Schrödinger equation,” Journal of Mathematical Chemistry, 2015. View at Publisher · View at Google Scholar
  • Kenan Mu, and T. E. Simos, “A Runge–Kutta type implicit high algebraic order two-step method with vanished phase-lag and its first, second, third and fourth derivatives for the numerical solution of coupled differential equations arising from the Schrödinger equation,” Journal of Mathematical Chemistry, 2015. View at Publisher · View at Google Scholar
  • Hang Ning, and T. E. Simos, “A low computational cost eight algebraic order hybrid method with vanished phase-lag and its first, second, third and fourth derivatives for the approximate solution of the Schrödinger equation,” Journal of Mathematical Chemistry, 2015. View at Publisher · View at Google Scholar
  • Zhou Zhou, and T. E. Simos, “A new two stage symmetric two-step method with vanished phase-lag and its first, second, third and fourth derivatives for the numerical solution of the radial Schrödinger equation,” Journal of Mathematical Chemistry, 2015. View at Publisher · View at Google Scholar
  • Jing Ma, and Simos, “A special high order runge-kutta type method for the solution of the schrödinger equation,” Applied Mathematics and Information Sciences, vol. 9, no. 5, pp. 2559–2577, 2015. View at Publisher · View at Google Scholar
  • Simos, “On the low algebraic order explicit methods with vanished phase-lag and its first and second derivative,” Applied Mathematics and Information Sciences, vol. 9, no. 6, pp. 2905–2916, 2015. View at Publisher · View at Google Scholar
  • Minjian Liang, and T. E. Simos, “A new four stages symmetric two-step method with vanished phase-lag and its first derivative for the numerical integration of the Schrödinger equation,” Journal of Mathematical Chemistry, 2016. View at Publisher · View at Google Scholar
  • Jianbin Zhao, and T. E. Simos, “A new fourteenth algebraic order finite difference method for the approximate solution of the Schrödinger equation,” Journal of Mathematical Chemistry, 2016. View at Publisher · View at Google Scholar
  • Maxim A. Medvedev, and T. E. Simos, “Two stages six-step method with eliminated phase-lag and its first, second, third and fourth derivatives for the approximation of the Schrödinger equation,” Journal of Mathematical Chemistry, vol. 55, no. 4, pp. 961–986, 2016. View at Publisher · View at Google Scholar
  • Fei Hui, and Simos, “Runge-Kutta type tenth algebraic order method with vanished phase-lag and its first, second, third, fourth and fifth derivatives for the numerical solution of the Schrödinger equation,” Applied Mathematics and Information Sciences, vol. 10, no. 1, pp. 143–153, 2016. View at Publisher · View at Google Scholar
  • Jingmei Zhou, and Simos, “Hybrid tenth algebraic order method with vanished phase-lag and its first, second, third and fourth derivatives for the approximate solution of the Schrödinger equation,” Applied Mathematics and Information Sciences, vol. 10, no. 1, pp. 193–202, 2016. View at Publisher · View at Google Scholar
  • Licheng Zhang, and Theodore E. Simos, “An Efficient Numerical Method for the Solution of the Schrödinger Equation,” Advances in Mathematical Physics, vol. 2016, pp. 1–20, 2016. View at Publisher · View at Google Scholar
  • Jie Fang, Chenglian Liu, and T. E. Simos, “A hybrid finite difference pair with maximum phase and stability properties,” Journal of Mathematical Chemistry, 2017. View at Publisher · View at Google Scholar
  • Junfeng Yao, and T. E. Simos, “New finite difference pair with optimized phase and stability properties,” Journal of Mathematical Chemistry, 2017. View at Publisher · View at Google Scholar
  • T.E. Simos, and Ch. Tsitouras, “A new family of 7 stages, eighth-order explicit Numerov-type methods,” Mathematical Methods in the Applied Sciences, 2017. View at Publisher · View at Google Scholar
  • Maxim A. Medvedev, and T. E. Simos, “A multistep method with optimal properties for second order differential equations,” Journal of Mathematical Chemistry, 2017. View at Publisher · View at Google Scholar
  • T. E. Simos, and Ch. Tsitouras, “Evolutionary generation of high-order, explicit, two-step methods for second-order linear IVPs,” Mathematical Methods in the Applied Sciences, 2017. View at Publisher · View at Google Scholar
  • Lan Yang, and T. E. Simos, “An efficient and economical high order method for the numerical approximation of the Schrödinger equation,” Journal of Mathematical Chemistry, 2017. View at Publisher · View at Google Scholar
  • Şeyhmus Yardimci, Esra Kir Arpat, and Çağla Can, “On the structure of discrete spectrum of a non-selfadjoint system of differential equations with integral boundary condition,” Journal of Mathematical Chemistry, vol. 55, no. 5, pp. 1202–1212, 2017. View at Publisher · View at Google Scholar
  • Dmitriy B. Berg, and T. E. Simos, “Three stages symmetric six-step method with eliminated phase-lag and its derivatives for the solution of the Schrödinger equation,” Journal of Mathematical Chemistry, 2017. View at Publisher · View at Google Scholar
  • Dmitriy B. Berg, and T. E. Simos, “An efficient six-step method for the solution of the Schrödinger equation,” Journal of Mathematical Chemistry, 2017. View at Publisher · View at Google Scholar
  • Dmitriy B. Berg, and T. E. Simos, “A new multistep finite difference pair for the Schrödinger equation and related problems,” Journal of Mathematical Chemistry, 2017. View at Publisher · View at Google Scholar
  • Zhiwei Wang, and T. E. Simos, “An economical eighth-order method for the approximation of the solution of the Schrödinger equation,” Journal of Mathematical Chemistry, 2017. View at Publisher · View at Google Scholar