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A Reliable Analytical Method for Solving Higher-Order Initial Value Problems

Author

Listed:
  • Omar Abu Arqub
  • Zaer Abo-Hammour
  • Ramzi Al-Badarneh
  • Shaher Momani

Abstract

In this article, a new analytical method has been devised to solve higher-order initial value problems for ordinary differential equations. This method was implemented to construct a series solution for higher-order initial value problems in the form of a rapidly convergent series with easily computable components using symbolic computation software. The proposed method is based on the Taylor series expansion which constructs an analytical solution in the form of a polynomial and reproduces the exact solution when the solution is polynomial. This technique is applied to a few test examples to illustrate the accuracy, efficiency, and applicability of the method. The results reveal that the method is very effective, straightforward, and simple.

Suggested Citation

  • Omar Abu Arqub & Zaer Abo-Hammour & Ramzi Al-Badarneh & Shaher Momani, 2013. "A Reliable Analytical Method for Solving Higher-Order Initial Value Problems," Discrete Dynamics in Nature and Society, Hindawi, vol. 2013, pages 1-12, December.
    • Handle: RePEc:hin:jnddns:673829
    DOI: 10.1155/2013/673829
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    Cited by:

    1. Samir A. El-Tantawy & Rasool Shah & Albandari W. Alrowaily & Nehad Ali Shah & Jae Dong Chung & Sherif. M. E. Ismaeel, 2023. "A Comparative Study of the Fractional-Order Belousov–Zhabotinsky System," Mathematics, MDPI, vol. 11(7), pages 1-15, April.
    2. Dubey, Ved Prakash & Singh, Jagdev & Alshehri, Ahmed M. & Dubey, Sarvesh & Kumar, Devendra, 2022. "Forecasting the behavior of fractional order Bloch equations appearing in NMR flow via a hybrid computational technique," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).

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