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Abstract and Applied Analysis
Volume 2012 (2012), Article ID 182536, 15 pages
http://dx.doi.org/10.1155/2012/182536
Research Article

New Stable Closed Newton-Cotes Trigonometrically Fitted Formulae for Long-Time Integration

1Department of Mathematics, College of Sciences, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia
2Laboratory of Computational Sciences, Department of Computer Science and Technology, Faculty of Sciences and Technology, University of Peloponnese, 221 00 Tripolis, Greece

Received 2 January 2012; Accepted 16 February 2012

Academic Editor: Muhammad Aslam Noor

Copyright © 2012 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 [23 citations]

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

  • Ibraheem Alolyan, and T.E. Simos, “A new high order two-step method with vanished phase-lag and its derivatives for the numerical integration of the Schrödinger equation,” Journal of Mathematical Chemistry, vol. 50, no. 9, pp. 2351–2373, 2012. View at Publisher · View at Google Scholar
  • T. E. Simos, “New high order multiderivative explicit four-step methods with vanished phase-lag and its derivatives for the approximate solution of the Schrödinger equation. Part I: Construction and theoretical analysis,” Journal of Mathematical Chemistry, vol. 51, no. 1, pp. 194–226, 2012. View at Publisher · View at Google Scholar
  • Ibraheem Alolyan, and T. E. Simos, “High order four-step hybrid method with vanished phase-lag and its derivatives for the approximate solution of the Schrödinger equation,” Journal of Mathematical Chemistry, vol. 51, no. 2, pp. 532–555, 2012. View at Publisher · View at Google Scholar
  • Norazak Senu, Mohamed Suleiman, Fudziah Ismail, and Norihan Md Arifin, “New 4(3) Pairs Diagonally Implicit Runge-Kutta-Nyström Method for Periodic IVPs,” Discrete Dynamics in Nature and Society, vol. 2012, pp. 1–20, 2012. View at Publisher · View at Google Scholar
  • Yonglei Fang, Qinghong Li, Qinghe Ming, and Kaimin Wang, “A New Optimized Runge-Kutta Pair for the Numerical Solution of the Radial Schrödinger Equation,” Abstract and Applied Analysis, vol. 2012, pp. 1–15, 2012. View at Publisher · View at Google Scholar
  • Yonglei Fang, Xiong You, and Zhaoxia Chen, “New Phase Fitted and Amplification Fitted Numerov-Type Methods for Periodic IVPs with Two Frequencies,” Abstract and Applied Analysis, vol. 2012, pp. 1–15, 2012. View at Publisher · View at Google Scholar
  • Ibraheem Alolyan, and T. E. Simos, “A new four-step hybrid type method with vanished phase-lag and its first derivatives for each level for the approximate integration of the Schrödinger equation,” Journal of Mathematical Chemistry, 2013. View at Publisher · View at Google Scholar
  • Ibraheem Alolyan, and T. E. Simos, “A new four-step Runge-Kutta type method with vanished phase-lag and its first, second and third derivatives for the numerical solution of the Schrodinger equation,” Journal Of Mathematical Chemistry, vol. 51, no. 5, pp. 1418–1445, 2013. View at Publisher · View at Google Scholar
  • G. A. Panopoulos, and T. E. Simos, “A new optimized symmetric 8-step semi-embedded predictor–corrector method for the numerical solution of the radial Schrödinger equation and related orbital problems,” Journal of Mathematical Chemistry, 2013. View at Publisher · View at Google Scholar
  • Dimitris F. Papadopoulos, and T. E. Simos, “A Modified Runge-Kutta-Nystrom Method by using Phase Lag Properties for the Numerical Solution of Orbital Problems,” Applied Mathematics & Information Sciences, vol. 7, no. 2, pp. 433–437, 2013. View at Publisher · View at Google Scholar
  • Coşar Gözükırmızı, and Metin Demiralp, “Probabilistic evolution approach for the solution of explicit autonomous ordinary differential equations. Part 1: Arbitrariness and equipartition theorem in Kronecker power series,” Journal of Mathematical Chemistry, vol. 52, no. 3, pp. 866–880, 2013. View at Publisher · View at Google Scholar
  • Ibraheem Alolyan, and T. E. Simos, “A Runge–Kutta type four-step method with vanished phase-lag and its first and second derivatives for each level for the numerical integration of the Schrödinger equation,” Journal of Mathematical Chemistry, vol. 52, no. 3, pp. 917–947, 2013. View at Publisher · View at Google Scholar
  • T. E. Simos, “An explicit four-step method with vanished phase-lag and its first and second derivatives,” Journal of Mathematical Chemistry, 2013. View at Publisher · View at Google Scholar
  • G. A. Panopoulos, and T. E. Simos, “An Optimized Symmetric 8-Step Semi-Embedded Predictor-Corrector Method for IVPs with Oscillating Solutions,” Applied Mathematics & Information Sciences, vol. 7, no. 1, pp. 73–80, 2013. View at Publisher · View at Google Scholar
  • Ghazala Akram, and Hamood Ur Rehman, “Solutions of a Class of Sixth Order Boundary Value Problems Using the Reproducing Kernel Space,” Abstract and Applied Analysis, vol. 2013, pp. 1–8, 2013. View at Publisher · View at Google Scholar
  • Jie Li, Honglei An, Huayong Zhu, Lincheng Shen, and Bin Fang, “Geometric Pseudospectral Method on SE(3) for Rigid-Body Dynamics with Application to Aircraft,” Mathematical Problems in Engineering, vol. 2013, pp. 1–16, 2013. View at Publisher · View at Google Scholar
  • Jingjun Zhao, Jingyu Xiao, and Yang Xu, “Stability and Convergence of an Effective Finite Element Method for Multiterm Fractional Partial Differential Equations,” Abstract and Applied Analysis, vol. 2013, pp. 1–10, 2013. View at Publisher · View at Google Scholar
  • Ibraheem Alolyan, and T. E. Simos, “A hybrid type four-step method with vanished phase-lag and its first, second and third derivatives for each level for the numerical integration of the Schrödinger equation,” Journal of Mathematical Chemistry, 2014. View at Publisher · View at Google Scholar
  • T. E. Simos, “An explicit linear six-step method with vanished phase-lag and its first derivative,” Journal of Mathematical Chemistry, 2014. View at Publisher · View at Google Scholar
  • Ibraheem Alolyan, and T. E. Simos, “A family of explicit linear six-step methods with vanished phase-lag and its first derivative,” Journal of Mathematical Chemistry, 2014. View at Publisher · View at Google Scholar
  • 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 hybrid four-step method with vanished phase-lag and its derivatives,” 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