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

Deepak Kumar, Ioannis K. Argyros and Janak Raj Sharma
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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

Mathematics, 2018, vol. 7, issue 1, 1-13

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.

Keywords: iterative methods; fast methods; local convergence; Banach space; complex dynamics (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2018
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