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New Family of Iterative Methods for Solving Nonlinear Models

Author

Listed:
  • Faisal Ali
  • Waqas Aslam
  • Kashif Ali
  • Muhammad Adnan Anwar
  • Akbar Nadeem

Abstract

We introduce a new family of iterative methods for solving mathematical models whose governing equations are nonlinear in nature. The new family gives several iterative schemes as special cases. We also give the convergence analysis of our proposed methods. In order to demonstrate the improved performance of newly developed methods, we consider some nonlinear equations along with two complex mathematical models. The graphical analysis for these models is also presented.

Suggested Citation

  • Faisal Ali & Waqas Aslam & Kashif Ali & Muhammad Adnan Anwar & Akbar Nadeem, 2018. "New Family of Iterative Methods for Solving Nonlinear Models," Discrete Dynamics in Nature and Society, Hindawi, vol. 2018, pages 1-12, April.
    • Handle: RePEc:hin:jnddns:9619680
    DOI: 10.1155/2018/9619680
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    Cited by:

    1. Shengfeng Li & Xiaobin Liu & Xiaofang Zhang, 2019. "A Few Iterative Methods by Using [1, n ]-Order Padé Approximation of Function and the Improvements," Mathematics, MDPI, vol. 7(1), pages 1-14, January.
    2. Kamsing Nonlaopon & Awais Gul Khan & Farah Ameen & Muhammad Uzair Awan & Clemente Cesarano, 2022. "Multi-Step Quantum Numerical Techniques for Finding the Solutions of Nonlinear Equations," Mathematics, MDPI, vol. 10(15), pages 1-17, July.
    3. Chein-Shan Liu & Essam R. El-Zahar & Chih-Wen Chang, 2023. "A Two-Dimensional Variant of Newton’s Method and a Three-Point Hermite Interpolation: Fourth- and Eighth-Order Optimal Iterative Schemes," Mathematics, MDPI, vol. 11(21), pages 1-21, November.

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