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Design and Complex Dynamics of Potra–Pták-Type Optimal Methods for Solving Nonlinear Equations and Its Applications

Author

Listed:
  • Prem B. Chand

    (Department of Mathematics, South Asian University, Akbar Bhawan, Chanakya Puri, New Delhi 110021, India
    These authors contributed equally to this work.)

  • Francisco I. Chicharro

    (Escuela Superior de Ingeniería y Tecnología, Universidad Internacional de La Rioja, Av. La Paz 137, 26006 Logroño, Spain
    These authors contributed equally to this work.)

  • Neus Garrido

    (Institute for Multidisciplinary Mathematics, Universitat Politècnica de València, Cno. de Vera s/n, 46022 València, Spain
    These authors contributed equally to this work.)

  • Pankaj Jain

    (Department of Mathematics, South Asian University, Akbar Bhawan, Chanakya Puri, New Delhi 110021, India
    These authors contributed equally to this work.)

Abstract

In this paper, using the idea of weight functions on the Potra–Pták method, an optimal fourth order method, a non optimal sixth order method, and a family of optimal eighth order methods are proposed. These methods are tested on some numerical examples, and the results are compared with some known methods of the corresponding order. It is proved that the results obtained from the proposed methods are compatible with other methods. The proposed methods are tested on some problems related to engineering and science. Furthermore, applying these methods on quadratic and cubic polynomials, their stability is analyzed by means of their basins of attraction.

Suggested Citation

  • Prem B. Chand & Francisco I. Chicharro & Neus Garrido & Pankaj Jain, 2019. "Design and Complex Dynamics of Potra–Pták-Type Optimal Methods for Solving Nonlinear Equations and Its Applications," Mathematics, MDPI, vol. 7(10), pages 1-21, October.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:10:p:942-:d:275431
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    References listed on IDEAS

    as
    1. Rajni Sharma & Ashu Bahl, 2015. "An Optimal Fourth Order Iterative Method for Solving Nonlinear Equations and Its Dynamics," Journal of Complex Analysis, Hindawi, vol. 2015, pages 1-9, November.
    2. F. I. Chicharro & A. Cordero & J. R. Torregrosa & M. P. Vassileva, 2017. "King-Type Derivative-Free Iterative Families: Real and Memory Dynamics," Complexity, Hindawi, vol. 2017, pages 1-15, October.
    Full references (including those not matched with items on IDEAS)

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