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Convergence Ball and Complex Geometry of an Iteration Function of Higher Order

Author

Listed:
  • Deepak Kumar

    (Department of Mathematics, Sant Longowal Institute of Engineering and Technology, Longowal-148106, Sangrur, India)

  • Ioannis K. Argyros

    (Department of Mathematics Sciences, Cameron University, Lawton, OK 73505, USA)

  • Janak Raj Sharma

    (Department of Mathematics, Sant Longowal Institute of Engineering and Technology, Longowal-148106, Sangrur, India)

Abstract

Higher-order derivatives are used to determine the convergence order of iterative methods. However, such derivatives are not present in the formulas. Therefore, the assumptions on the higher-order derivatives of the function restrict the applicability of methods. Our convergence analysis of an eighth-order method uses only the derivative of order one. The convergence results so obtained are applied to some real problems, which arise in science and engineering. Finally, stability of the method is checked through complex geometry shown by drawing basins of attraction of the solutions.

Suggested Citation

  • Deepak Kumar & Ioannis K. Argyros & Janak Raj Sharma, 2018. "Convergence Ball and Complex Geometry of an Iteration Function of Higher Order," Mathematics, MDPI, vol. 7(1), pages 1-13, December.
    • Handle: RePEc:gam:jmathe:v:7:y:2018:i:1:p:28-:d:193789
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    References listed on IDEAS

    as
    1. Alicia Cordero & Esther Gómez & Juan R. Torregrosa, 2017. "Efficient High-Order Iterative Methods for Solving Nonlinear Systems and Their Application on Heat Conduction Problems," Complexity, Hindawi, vol. 2017, pages 1-11, January.
    2. Rostamy, Davoud & Bakhtiari, Parisa, 2015. "New efficient multipoint iterative methods for solving nonlinear systems," Applied Mathematics and Computation, Elsevier, vol. 266(C), pages 350-356.
    3. Alzahrani, Abdullah Khamis Hassan & Behl, Ramandeep & Alshomrani, Ali Saleh, 2018. "Some higher-order iteration functions for solving nonlinear models," Applied Mathematics and Computation, Elsevier, vol. 334(C), pages 80-93.
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