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

Prem B. Chand, Francisco I. Chicharro, Neus Garrido and Pankaj Jain
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Prem B. Chand: Department of Mathematics, South Asian University, Akbar Bhawan, Chanakya Puri, New Delhi 110021, India
Francisco I. Chicharro: Escuela Superior de Ingeniería y Tecnología, Universidad Internacional de La Rioja, Av. La Paz 137, 26006 Logroño, Spain
Neus Garrido: Institute for Multidisciplinary Mathematics, Universitat Politècnica de València, Cno. de Vera s/n, 46022 València, Spain
Pankaj Jain: Department of Mathematics, South Asian University, Akbar Bhawan, Chanakya Puri, New Delhi 110021, India

Mathematics, 2019, vol. 7, issue 10, 1-21

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.

Keywords: nonlinear equations; Potra–Pták method; optimal methods; weight function; basin of attraction; engineering applications (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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