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Iterative Multistep Reproducing Kernel Hilbert Space Method for Solving Strongly Nonlinear Oscillators

Author

Listed:
  • Banan Maayah
  • Samia Bushnaq
  • Shaher Momani
  • Omar Abu Arqub

Abstract

A new algorithm called multistep reproducing kernel Hilbert space method is represented to solve nonlinear oscillator’s models. The proposed scheme is a modification of the reproducing kernel Hilbert space method, which will increase the intervals of convergence for the series solution. The numerical results demonstrate the validity and the applicability of the new technique. A very good agreement was found between the results obtained using the presented algorithm and the Runge‐Kutta method, which shows that the multistep reproducing kernel Hilbert space method is very efficient and convenient for solving nonlinear oscillator’s models.

Suggested Citation

  • 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).
    • Handle: RePEc:wly:jnlamp:v:2014:y:2014:i:1:n:758195
    DOI: 10.1155/2014/758195
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    References listed on IDEAS

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    1. 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.
    2. Samia Bushnaq & Banan Maayah & Shaher Momani & Ahmed Alsaedi, 2014. "A Reproducing Kernel Hilbert Space Method for Solving Systems of Fractional Integrodifferential Equations," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-6, March.
    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).
    4. Shaher Momani, 2004. "Analytical Approximate Solutions Of Nonlinear Oscillators By The Modified Decomposition Method," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 15(07), pages 967-979.
    5. 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.
    6. Samia Bushnaq & Banan Maayah & Shaher Momani & Ahmed Alsaedi, 2014. "A Reproducing Kernel Hilbert Space Method for Solving Systems of Fractional Integrodifferential Equations," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    7. 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).
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