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Memory in a New Variant of King’s Family for Solving Nonlinear Systems

Author

Listed:
  • Munish Kansal

    (School of Mathematics, Thapar Institute of Engineering and Technology University, Patiala 147004, India)

  • Alicia Cordero

    (Institute for Multidisciplinary Mathematics, Universitat Politècnica de Valenència, Camino de Vera s/n, 46022 València, Spain)

  • Sonia Bhalla

    (Department of Mathematics, Chandigarh University, Gharuan 140413, India)

  • Juan R. Torregrosa

    (Institute for Multidisciplinary Mathematics, Universitat Politècnica de Valenència, Camino de Vera s/n, 46022 València, Spain)

Abstract

In the recent literature, very few high-order Jacobian-free methods with memory for solving nonlinear systems appear. In this paper, we introduce a new variant of King’s family with order four to solve nonlinear systems along with its convergence analysis. The proposed family requires two divided difference operators and to compute only one inverse of a matrix per iteration. Furthermore, we have extended the proposed scheme up to the sixth-order of convergence with two additional functional evaluations. In addition, these schemes are further extended to methods with memory. We illustrate their applicability by performing numerical experiments on a wide variety of practical problems, even big-sized. It is observed that these methods produce approximations of greater accuracy and are more efficient in practice, compared with the existing methods.

Suggested Citation

  • Munish Kansal & Alicia Cordero & Sonia Bhalla & Juan R. Torregrosa, 2020. "Memory in a New Variant of King’s Family for Solving Nonlinear Systems," Mathematics, MDPI, vol. 8(8), pages 1-15, July.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:8:p:1251-:d:392695
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    References listed on IDEAS

    as
    1. 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.
    2. Noor, Muhammad Aslam & Waseem, Muhammad & Noor, Khalida Inayat, 2015. "New iterative technique for solving a system of nonlinear equations," Applied Mathematics and Computation, Elsevier, vol. 271(C), pages 446-466.
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