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Some Recent Modifications of Fixed Point Iterative Schemes for Computing Zeros of Nonlinear Equations

Author

Listed:
  • Gul Sana
  • Muhammad Aslam Noor
  • Mahmood Ul Hassan
  • Zakia Hammouch

Abstract

In computational mathematics, it is a matter of deep concern to recognize which of the given iteration schemes converges quickly with lesser error to the desired solution. Fixed point iterative schemes are constructed to be used for solving equations emerging in many fields of science and engineering. These schemes reformulate a nonlinear equation f(s) = 0 into a fixed point equation of the form s = g(s) ; such application determines the solution of the original equation via the support of fixed point iterative method and is subject to existence and uniqueness. In this manuscript, we introduce a new modified family of fixed point iterative schemes for solving nonlinear equations which generalize further recursive methods as particular cases. We also prove the convergence of our suggested schemes. We also consider some of the mathematical models which are categorically nonlinear in essence to authenticate the performance and effectiveness of these schemes which can be seen as an expansion and rationalization of some existing techniques.

Suggested Citation

  • Gul Sana & Muhammad Aslam Noor & Mahmood Ul Hassan & Zakia Hammouch, 2022. "Some Recent Modifications of Fixed Point Iterative Schemes for Computing Zeros of Nonlinear Equations," Complexity, John Wiley & Sons, vol. 2022(1).
    • Handle: RePEc:wly:complx:v:2022:y:2022:i:1:n:4331899
    DOI: 10.1155/2022/4331899
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    References listed on IDEAS

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    1. Sachin Bhalekar & Varsha Daftardar-Gejji, 2011. "Convergence of the New Iterative Method," International Journal of Differential Equations, Hindawi, vol. 2011, pages 1-10, November.
    2. Noor, Muhammad Aslam & Waseem, Muhammad & Noor, Khalida Inayat & Ali, Muhammad Aamir, 2015. "New iterative technique for solving nonlinear equations," Applied Mathematics and Computation, Elsevier, vol. 265(C), pages 1115-1125.
    3. Shin Min Kang & Arif Rafiq & Young Chel Kwun, 2013. "A New Second‐Order Iteration Method for Solving Nonlinear Equations," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    4. Faisal Ali & Waqas Aslam & Imran Khalid & Akbar Nadeem & Antonio Di Crescenzo, 2020. "Iteration Methods with an Auxiliary Function for Nonlinear Equations," Journal of Mathematics, Hindawi, vol. 2020, pages 1-15, October.
    5. Shin Min Kang & Arif Rafiq & Young Chel Kwun, 2013. "A New Second-Order Iteration Method for Solving Nonlinear Equations," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-4, April.
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