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Abstract and Applied Analysis
Volume 2013, Article ID 704137, 6 pages
http://dx.doi.org/10.1155/2013/704137
Research Article

Perturbation-Iteration Method for First-Order Differential Equations and Systems

1Department of Mathematics, Nevsehir University, 50300 Nevsehir, Turkey
2Department of Mechanical Engineering, Celal Bayar University, Muradiye, 45140 Manisa, Turkey

Received 16 March 2013; Revised 18 April 2013; Accepted 19 April 2013

Academic Editor: Yisheng Song

Copyright © 2013 Mehmet Şenol et al. 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 [11 citations]

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

  • Necdet Bildik, and Sinan Deniz, “Modification of perturbation-iteration method to solve different types of nonlinear differential equations,” vol. 1798, pp. 020027, . View at Publisher · View at Google Scholar
  • Mehmet Şenol, and I. Timuçin Dolapci, “On the Perturbation-Iteration Algorithm for Fractional Differential Equations,” Journal of King Saud University - Science, 2015. View at Publisher · View at Google Scholar
  • Sinan Deniz, and Necdet Bildi, “Optimal Perturbation Iteration Method for Bratu-Type Problems,” Journal of King Saud University - Science, 2016. View at Publisher · View at Google Scholar
  • Necdet Bildik, and Sinan Deniz, “Comparative Study between Optimal Homotopy Asymptotic Method and Perturbation-Iteration Technique for Different Types of Nonlinear Equations,” Iranian Journal of Science and Technology, Transactions A: Science, 2016. View at Publisher · View at Google Scholar
  • Mehmet Pakdemirli, “Application of the perturbation iteration method to boundary layer type problems,” Springerplus, vol. 5, 2016. View at Publisher · View at Google Scholar
  • Sinan Deniz, “Optimal Perturbation Iteration Method for Solving Nonlinear Heat Transfer Equations,” Journal of Heat Transfer, vol. 139, no. 7, 2017. View at Publisher · View at Google Scholar
  • M. D. S. Aliyu, “A Successive Relaxation Approach for Solving the Coupled Hamilton–Jacobi–Isaacs Equations in Nonzero-Sum Differential Games of Affine Nonlinear Systems,” International Journal of Applied and Computational Mathematics, 2017. View at Publisher · View at Google Scholar
  • Mehmet Pakdemirli, “Perturbation–iteration method for strongly nonlinear vibrations,” Journal of Vibration and Control, vol. 23, no. 6, pp. 959–969, 2017. View at Publisher · View at Google Scholar
  • Necdet Bildik, and Sinan Deniz, “A new efficient method for solving delay differential equations and a comparison with other methods,” The European Physical Journal Plus, vol. 132, no. 1, 2017. View at Publisher · View at Google Scholar
  • Sinan Deniz, and Necdet Bildik, “Applications of optimal perturbation iteration method for solving nonlinear differential equations,” AIP Conference Proceedings, vol. 1798, 2017. View at Publisher · View at Google Scholar
  • Mehmet Şenol, Hamed Daei Kasmaei, and Marwan Alquran, “On the comparison of perturbation-iteration algorithm and residual power series method to solve fractional Zakharov-Kuznetsov equation,” Results in Physics, vol. 9, pp. 321–327, 2018. View at Publisher · View at Google Scholar