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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, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnljam:v:2014:y:2014:i:1:n:135465
    DOI: 10.1155/2014/135465
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    References listed on IDEAS

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    1. Omar Abu Arqub & Mohammed Al-Smadi & Shaher Momani, 2012. "Application of Reproducing Kernel Method for Solving Nonlinear Fredholm-Volterra Integrodifferential Equations," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-16, September.
    2. Ruyun Ma & Tianlan Chen & Yanqiong Lu, 2010. "Positive Periodic Solutions of Nonlinear First-Order Functional Difference Equations," Discrete Dynamics in Nature and Society, Hindawi, vol. 2010, pages 1-15, January.
    3. Omar Abu Arqub & Mohammed Al-Smadi & Shaher Momani, 2012. "Application of Reproducing Kernel Method for Solving Nonlinear Fredholm‐Volterra Integrodifferential Equations," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
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    Cited by:

    1. Banan Maayah & Samia Bushnaq & Shaher Momani & Omar Abu Arqub, 2014. "Iterative Multistep Reproducing Kernel Hilbert Space Method for Solving Strongly Nonlinear Oscillators," Advances in Mathematical Physics, John Wiley & Sons, vol. 2014(1).

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