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

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  • Mohammed AL-Smadi
  • Omar Abu Arqub
  • Ahmad El-Ajou

Abstract

The objective of this paper is to present a numerical iterative method for solving systems of first-order ordinary differential equations subject to periodic boundary conditions. This iterative technique is based on the use of the reproducing kernel Hilbert space method in which every function satisfies the periodic boundary conditions. The present method is accurate, needs less effort to achieve the results, and is especially developed for nonlinear case. Furthermore, the present method enables us to approximate the solutions and their derivatives at every point of the range of integration. Indeed, three numerical examples are provided to illustrate the effectiveness of the present method. Results obtained show that the numerical scheme is very effective and convenient for solving systems of first-order ordinary differential equations with periodic boundary conditions.

Suggested Citation

  • Mohammed AL-Smadi & Omar Abu Arqub & Ahmad El-Ajou, 2014. "A Numerical Iterative Method for Solving Systems of First-Order Periodic Boundary Value Problems," Journal of Applied Mathematics, Hindawi, vol. 2014, pages 1-10, March.
    • Handle: RePEc:hin:jnljam:135465
    DOI: 10.1155/2014/135465
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    1. Bentout, Soufiane & Djilali, Salih, 2023. "Asymptotic profiles of a nonlocal dispersal SIR epidemic model with treat-age in a heterogeneous environment," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 203(C), pages 926-956.
    2. Bukhari, Ayaz Hussain & Raja, Muhammad Asif Zahoor & Rafiq, Naila & Shoaib, Muhammad & Kiani, Adiqa Kausar & Shu, Chi-Min, 2022. "Design of intelligent computing networks for nonlinear chaotic fractional Rossler system," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).
    3. Khan, Zeshan Aslam & Chaudhary, Naveed Ishtiaq & Raja, Muhammad Asif Zahoor, 2022. "Generalized fractional strategy for recommender systems with chaotic ratings behavior," Chaos, Solitons & Fractals, Elsevier, vol. 160(C).
    4. Muhammad, Yasir & Khan, Nusrat & Awan, Saeed Ehsan & Raja, Muhammad Asif Zahoor & Chaudhary, Naveed Ishtiaq & Kiani, Adiqa Kausar & Ullah, Farman & Shu, Chi-Min, 2022. "Fractional memetic computing paradigm for reactive power management involving wind-load chaos and uncertainties," Chaos, Solitons & Fractals, Elsevier, vol. 161(C).

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