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Mathematical Problems in Engineering
Volume 2013 (2013), Article ID 832074, 10 pages
http://dx.doi.org/10.1155/2013/832074
Research Article

A Computational Method for Two-Point Boundary Value Problems of Fourth-Order Mixed Integrodifferential Equations

1Department of Mathematics, Tafila Technical University, Tafila 66110, Jordan
2Department of Mathematics, Al-Balqa Applied University, Salt 19117, Jordan
3Department of Mathematics, University of Jordan, Amman 11942, Jordan

Received 27 July 2012; Accepted 29 January 2013

Academic Editor: Hung Nguyen-Xuan

Copyright © 2013 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 [39 citations]

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

  • Omar Abu Arqub, Mohammed Al-Smadi, and Nabil Shawagfeh, “Solving Fredholm integro–differential equations using reproducing kernel Hilbert space method,” Applied Mathematics and Computation, vol. 219, no. 17, pp. 8938–8948, 2013. View at Publisher · View at Google Scholar
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  • Omar Abu Arqub, and Mohammed Al-Smadi, “Numerical algorithm for solving two-point, second-order periodic boundary value problems for mixed integro-differential equations,” Applied Mathematics and Computation, vol. 243, pp. 911–922, 2014. View at Publisher · View at Google Scholar
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  • Omar Abu Arqub, Ahmad El-Ajou, Zeyad Al Zhour, and Shaher Momani, “Multiple Solutions of Nonlinear Boundary Value Problems of Fractional Order: A New Analytic Iterative Technique,” Entropy, vol. 16, no. 1, pp. 471–493, 2014. View at Publisher · View at Google Scholar
  • Zaer Abo-Hammour, Omar Abu Arqub, Othman Alsmadi, Shaher Momani, and Ahmed Alsaedi, “An optimization algorithm for solving systems of singular boundary value problems,” Applied Mathematics and Information Sciences, vol. 8, no. 6, pp. 2809–2821, 2014. View at Publisher · View at Google Scholar
  • Mohammed AL-Smadi, Omar Abu Arqub, and Ahmad El-Ajou, “A Numerical Iterative Method for Solving Systems of First-Order Periodic Boundary Value Problems,” Journal of Applied Mathematics, vol. 2014, pp. 1–10, 2014. View at Publisher · View at Google Scholar
  • Shaher Momani, Asad Freihat, and Mohammed AL-Smadi, “Analytical Study of Fractional-Order Multiple Chaotic FitzHugh-Nagumo Neurons Model Using Multistep Generalized Differential Transform Method,” Abstract and Applied Analysis, vol. 2014, pp. 1–10, 2014. View at Publisher · View at Google Scholar
  • Zaer Abo-Hammour, Omar Abu Arqub, Shaher Momani, and Nabil Shawagfeh, “Optimization Solution of Troesch’s and Bratu’s Problems of Ordinary Type Using Novel Continuous Genetic Algorithm,” Discrete Dynamics in Nature and Society, vol. 2014, pp. 1–15, 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
  • Radwan Abu-Gdairi, Mohammed Al-Smadi, and Ghaleb Gumah, “An expansion iterative technique for handling fractional differential equations using fractional power series scheme,” Journal of Mathematics and Statistics, vol. 11, no. 2, pp. 29–38, 2015. 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
  • 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
  • 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
  • Shaher Momani, Omar Abu Arqub, Ma'mon Abu Hammad, and Zaer S. Abo-Hammour, “A residual power series technique for solving systems of initial value problems,” Applied Mathematics and Information Sciences, vol. 10, no. 2, pp. 765–775, 2016. View at Publisher · View at Google Scholar
  • Eman Abuteen, Asad Freihat, Hammad Khalil, Rahmat Ali Khan, and Mohammed Al-Smadi, “Approximate series solution of nonlinear, fractional Klein-Gordon equations using fractional reduced differential transform method,” Journal of Mathematics and Statistics, vol. 12, no. 1, pp. 23–33, 2016. View at Publisher · View at Google Scholar
  • Mohammed Al-Smadi, “Simplified iterative reproducing kernel method for handling time-fractional BVPs with error estimation,” Ain Shams Engineering Journal, 2017. View at Publisher · View at Google Scholar
  • Khalid Majeed, Zaheer Masood, Raza Samar, and Muhammad Asif Zahoor Raja, “A genetic algorithm optimized Morlet wavelet artificial neural network to study the dynamics of nonlinear Troesch’s system,” Applied Soft Computing, vol. 56, pp. 420–435, 2017. 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
  • Mohammed Al-Smadi, Asad Freihat, Hammad Khalil, Shaher Momani, and Rahmat Ali Khan, “Numerical Multistep Approach for Solving Fractional Partial Differential Equations,” International Journal of Computational Methods, vol. 14, no. 03, pp. 1750029, 2017. View at Publisher · View at Google Scholar
  • Muhammad Zaini Ahmad, Shaher Momani, Banan Maayah, and Asia Khalaf Albzeirat, “Numerical solution of second-order fuzzy differential equation of integer and fractional order using reproducing kernel hilbert space method tools,” Far East Journal of Mathematical Sciences, vol. 101, no. 6, pp. 1327–1351, 2017. View at Publisher · View at Google Scholar
  • Muhammad Asif Zahoor Raja, Fiaz Hussain Shah, Eman Salem Alaidarous, and Muhammad Ibrahim Syam, “Design of bio-inspired heuristic technique integrated with interior-point algorithm to analyze the dynamics of heartbeat model,” Applied Soft Computing, vol. 52, pp. 605–629, 2017. View at Publisher · View at Google Scholar
  • Muhammad Asif Zahoor Raja, Fiaz Hussain Shah, and Muhammad Ibrahim Syam, “Intelligent computing approach to solve the nonlinear Van der Pol system for heartbeat model,” Neural Computing and Applications, 2017. View at Publisher · View at Google Scholar
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