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A New Jarratt-Type Fourth-Order Method for Solving System of Nonlinear Equations and Applications

Author

Listed:
  • Moin-ud-Din Junjua
  • Saima Akram
  • Nusrat Yasmin
  • Fiza Zafar

Abstract

Solving systems of nonlinear equations plays a major role in engineering problems. We present a new family of optimal fourth-order Jarratt-type methods for solving nonlinear equations and extend these methods to solve system of nonlinear equations. Convergence analysis is given for both cases to show that the order of the new methods is four. Cost of computations, numerical tests, and basins of attraction are presented which illustrate the new methods as better alternates to previous methods. We also give an application of the proposed methods to well-known Burger's equation.

Suggested Citation

  • Moin-ud-Din Junjua & Saima Akram & Nusrat Yasmin & Fiza Zafar, 2015. "A New Jarratt-Type Fourth-Order Method for Solving System of Nonlinear Equations and Applications," Journal of Applied Mathematics, Hindawi, vol. 2015, pages 1-14, March.
    • Handle: RePEc:hin:jnljam:805278
    DOI: 10.1155/2015/805278
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    Cited by:

    1. Ramandeep Behl & Alicia Cordero & Juan R. Torregrosa & Ali Saleh Alshomrani, 2018. "New Iterative Methods for Solving Nonlinear Problems with One and Several Unknowns," Mathematics, MDPI, vol. 6(12), pages 1-17, December.
    2. Janak Raj Sharma & Deepak Kumar & Ioannis K. Argyros, 2019. "Local Convergence and Attraction Basins of Higher Order, Jarratt-Like Iterations," Mathematics, MDPI, vol. 7(12), pages 1-16, December.
    3. José J. Padilla & Francisco I. Chicharro & Alicia Cordero & Alejandro M. Hernández-Díaz & Juan R. Torregrosa, 2024. "A Class of Efficient Sixth-Order Iterative Methods for Solving the Nonlinear Shear Model of a Reinforced Concrete Beam," Mathematics, MDPI, vol. 12(3), pages 1-16, February.
    4. Ioannis K. Argyros & Ramandeep Behl, 2019. "Ball Comparison for Some Efficient Fourth Order Iterative Methods Under Weak Conditions," Mathematics, MDPI, vol. 7(1), pages 1-14, January.

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