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Journal of Applied Mathematics
Volume 2014, Article ID 135465, 10 pages
http://dx.doi.org/10.1155/2014/135465
Research Article

A Numerical Iterative Method for Solving Systems of First-Order Periodic Boundary Value Problems

1Applied Science Department, Ajloun College, Al-Balqa Applied University, Ajloun 26816, Jordan
2Department of Mathematics, Al-Balqa Applied University, Salt 19117, Jordan

Received 12 September 2013; Accepted 11 February 2014; Published 25 March 2014

Academic Editor: Hak-Keung Lam

Copyright © 2014 Mohammed AL-Smadi 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 [20 citations]

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

  • Shaher Momani, Omar Abu Arqub, Tasawar Hayat, and Hamed Al-Sulami, “A computational method for solving periodic boundary value problems for integro-differential equations of Fredholm–Volterra type,” Applied Mathematics and Computation, vol. 240, pp. 229–239, 2014. View at Publisher · View at Google Scholar
  • Omar Abu Arqub, and Zaer Abo-Hammour, “Numerical solution of systems of second-order boundary value problems using continuous genetic algorithm,” Information Sciences, 2014. View at Publisher · View at Google Scholar
  • Iryna Komashynska, and Mohammed AL-Smadi, “Iterative Reproducing Kernel Method for Solving Second-Order Integrodifferential Equations of Fredholm Type,” Journal of Applied Mathematics, vol. 2014, pp. 1–11, 2014. View at Publisher · View at Google Scholar
  • Banan Maayah, Samia Bushnaq, Shaher Momani, and Omar Abu Arqub, “Iterative Multistep Reproducing Kernel Hilbert Space Method for Solving Strongly Nonlinear Oscillators,” Advances in Mathematical Physics, vol. 2014, pp. 1–7, 2014. View at Publisher · View at Google Scholar
  • Pei Dang, Jinyuan Du, and Tao Qian, “Boundary value problems for periodic analytic functions,” Boundary Value Problems, vol. 2015, no. 1, 2015. View at Publisher · View at Google Scholar
  • Omar Abu Arqub, Mohammed AL-Smadi, Shaher Momani, and Tasawar Hayat, “Numerical solutions of fuzzy differential equations using reproducing kernel Hilbert space method,” Soft Computing, 2015. View at Publisher · View at Google Scholar
  • Omar Abu Arqub, “Adaptation of reproducing kernel algorithm for solving fuzzy Fredholm–Volterra integrodifferential equations,” Neural Computing and Applications, vol. 28, no. 7, pp. 1591–1610, 2015. View at Publisher · View at Google Scholar
  • Khaled Moaddy, Mohammed AL-Smadi, and Ishak Hashim, “A Novel Representation of the Exact Solution for Differential Algebraic Equations System Using Residual Power-Series Method,” Discrete Dynamics in Nature and Society, vol. 2015, pp. 1–12, 2015. View at Publisher · View at Google Scholar
  • Omar Abu Arqub, “Reproducing Kernel Algorithm for the Analytical-Numerical Solutions of Nonlinear Systems of Singular Periodic Boundary Value Problems,” Mathematical Problems in Engineering, vol. 2015, pp. 1–13, 2015. View at Publisher · View at Google Scholar
  • Mousa Ababneh, “Analytical solutions of first-order, periodic boundary value problem,” International Journal of Mathematical Analysis, vol. 9, no. 25-28, pp. 1385–1398, 2015. View at Publisher · View at Google Scholar
  • Ayed Hussein Al E'Damat, “Analytical-numerical method for solving a class of two-point boundary value problems,” International Journal of Mathematical Analysis, vol. 9, no. 37-40, pp. 1987–2002, 2015. View at Publisher · View at Google Scholar
  • Iryna Komashynska, Ali Ateiwi, Sadoon Al-Obaidy, and Mohammed Al-Smadi, “Approximate analytical solution by residual power series method for system of Fredholm integral equations,” Applied Mathematics and Information Sciences, vol. 10, no. 3, pp. 975–985, 2016. View at Publisher · View at Google Scholar
  • Radwan Abu-Gdairi, Rahmat Ali Khan, Asad Freihat, Hammad Khalil, Eman Abuteen, and Mohammed Al-Smadi, “Fitted reproducing kernel method for solving a class of third-order periodic boundary value problems,” American Journal of Applied Sciences, vol. 13, no. 5, pp. 501–510, 2016. View at Publisher · View at Google Scholar
  • Mohammed Al-Smadi, Omar Abu Arqub, Nabil Shawagfeh, and Shaher Momani, “Numerical investigations for systems of second-order periodic boundary value problems using reproducing kernel method,” Applied Mathematics and Computation, vol. 291, pp. 137–148, 2016. View at Publisher · View at Google Scholar
  • Ghaleb Gumah, Khaled Moaddy, Mohammed Al-Smadi, and Ishak Hashim, “Solutions to Uncertain Volterra Integral Equations by Fitted Reproducing Kernel Hilbert Space Method,” Journal of Function Spaces, vol. 2016, pp. 1–11, 2016. View at Publisher · View at Google Scholar
  • Ghaleb Gumah, Hammad Khalil, Rahmat Ali Khan, Rania Saadeh, and Mohammed Al-Smadi, “Numerical investigation for solving two-point fuzzy boundary value problems by reproducing kernel approach,” Applied Mathematics and Information Sciences, vol. 10, no. 6, pp. 2117–2129, 2016. View at Publisher · View at Google Scholar
  • Iryna Komashynska, Omar Abu Arqub, Mohammed Al-Smadi, and Shaher Momani, “An efficient analytical method for solving singular initial value problems of nonlinear systems,” Applied Mathematics and Information Sciences, vol. 10, no. 2, pp. 647–656, 2016. View at Publisher · View at Google Scholar
  • Samia Bushnaq, Banan Maayah, and Asma AlHabees, “Application of multistep reproducing kernel hilbert space method for solving giving up smoking model,” International Journal of Pure and Applied Mathematics, vol. 109, no. 2, pp. 311–324, 2016. View at Publisher · View at Google Scholar
  • Shaher Momani, Marwan Kutbi, Omar Abu Arqub, and Saleh Al-Mezel, “A novel iterative numerical algorithm for the solutions of systems of fuzzy initial value problems,” Applied Mathematics and Information Sciences, vol. 11, no. 4, pp. 1059–1074, 2017. View at Publisher · View at Google Scholar
  • Mehmet Giyas Sakar, “Iterative reproducing kernel Hilbert spaces method for Riccati differential equations,” Journal of Computational and Applied Mathematics, vol. 309, pp. 163–174, 2017. View at Publisher · View at Google Scholar