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Mathematical Problems in Engineering
Volume 2011, Article ID 724927, 19 pages
http://dx.doi.org/10.1155/2011/724927
Research Article

On the Solutions of Nonlinear Higher-Order Boundary Value Problems by Using Differential Transformation Method and Adomian Decomposition Method

Department of Mathematics, University Putra Malaysia, 43400 UPM Serdang, Selangor, Malaysia

Received 8 November 2010; Accepted 7 February 2011

Academic Editor: Alexei Mailybaev

Copyright © 2011 Che Haziqah Che Hussin and Adem Kiliçman. 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 [15 citations]

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

  • Javed Ali, S. Islam, Hamid Khan, and Syed Inayat Ali Shah, “The Optimal Homotopy Asymptotic Method for the Solution of Higher-Order Boundary Value Problems in Finite Domains,” Abstract and Applied Analysis, vol. 2012, pp. 1–14, 2012. View at Publisher · View at Google Scholar
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  • Omer Altun, and Adem Kilicman, “On the solutions of some boundary value problems by using differential transformation method with convolution terms,” Filomat, vol. 26, no. 5, pp. 917–928, 2012. View at Publisher · View at Google Scholar
  • Abdelhalim Ebaid, “On a new differential transformation method for solving nonlinear differential equations,” Asian-European Journal of Mathematics, vol. 6, no. 4, 2013. View at Publisher · View at Google Scholar
  • Omer Altun, and Adem Kiliçman, “On solutions of matrix initial value problems by using differential transform method and convolution,” AIP Conference Proceedings, vol. 1557, pp. 191–194, 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
  • A. Kazemi Nasab, A. Kilicman, Z. Pashazadeh Atabakan, and S. Abbasbandy, “Chebyshev Wavelet Finite Difference Method: A New Approach for Solving Initial and Boundary Value Problems of Fractional Order,” Abstract and Applied Analysis, 2013. View at Publisher · View at Google Scholar
  • Adem Kilicman, and Omer Altun, “On higher-order boundary value problems by using differential transformation method with convolution terms,” Journal of The Franklin Institute-Engineering and Applied Mathematics, vol. 351, no. 2, pp. 631–642, 2014. View at Publisher · View at Google Scholar
  • Che Haziqah Che Hussin, Adem Kilicman, Arif Mandangan, Che Haziqah Che Hussin, Adem Kilicman, and Arif Mandangan, “Comparing Linear and Nonlinear Differential Equations of Differential Transformation Method by Other Numerical Methods,” Proceedings of The 3rd International Conference on Mathematical Sciences, vol. 1602, pp. 43–49, 2014. View at Publisher · View at Google Scholar
  • Che Haziqah Che Hussin, Arif Mandangan, Che Haziqah Che Hussin, and Arif Mandangan, “Solving Eighth-order Boundary Value Problems Using Differential Transformation Method,” International Conference On Quantitative Sciences And Its Applications (Icoqsia 2014), vol. 1635, pp. 99–106, 2014. View at Publisher · View at Google Scholar
  • Saha Ray, “A new analytical modelling for nonlocal generalized Riesz fractional sine-Gordon equation,” Journal of King Saud University - Science, vol. 28, no. 1, pp. 48–54, 2016. View at Publisher · View at Google Scholar
  • Arvind Patel, and Vineesh Kumar, “Dark and kink soliton solutions of the generalized ZK–BBM equation by iterative scheme,” Chinese Journal of Physics, vol. 56, no. 3, pp. 819–829, 2018. View at Publisher · View at Google Scholar
  • Liaqat Ali, Saeed Islam, Taza Gul, Muhammad Altaf Khan, and Ebenezer Bonyah, “Solutions of nonlinear real world problems by a new analytical technique,” Heliyon, vol. 4, no. 11, pp. e00913, 2018. View at Publisher · View at Google Scholar
  • Taza Gul, Ali Saleh Alshomrani, Liaqat Ali, Saeed Islam, and Murad Ullah, “A new analytical approach for solving nonlinear boundary value problems arising in nonlinear phenomena,” Filomat, vol. 32, no. 7, pp. 2489–2497, 2018. View at Publisher · View at Google Scholar
  • Adem Kili�man, Djumaklich Amanov, and Gafurjan Ibragimov, “On a generalization of the initial-boundary problem for the vibrating string equation,” Symmetry, vol. 11, no. 1, 2019. View at Publisher · View at Google Scholar