A New High-Order Jacobian-Free Iterative Method with Memory for Solving Nonlinear Systems

Ramandeep Behl, Alicia Cordero, Juan R. Torregrosa and Sonia Bhalla
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Ramandeep Behl: Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia
Alicia Cordero: Institute for Multidisciplinary Mathematics, Universitat Politècnica de València, 46022 València, Spain
Juan R. Torregrosa: Institute for Multidisciplinary Mathematics, Universitat Politècnica de València, 46022 València, Spain
Sonia Bhalla: Department of Mathematics, Chandigarh University, Mohali 140413, India

Mathematics, 2021, vol. 9, issue 17, 1-16

Abstract: We used a Kurchatov-type accelerator to construct an iterative method with memory for solving nonlinear systems, with sixth-order convergence. It was developed from an initial scheme without memory, with order of convergence four. There exist few multidimensional schemes using more than one previous iterate in the very recent literature, mostly with low orders of convergence. The proposed scheme showed its efficiency and robustness in several numerical tests, where it was also compared with the existing procedures with high orders of convergence. These numerical tests included large nonlinear systems. In addition, we show that the proposed scheme has very stable qualitative behavior, by means of the analysis of an associated multidimensional, real rational function and also by means of a comparison of its basin of attraction with those of comparison methods.

Keywords: nonlinear systems of equations; iterative methods; acceleration of convergence; efficiency; stability (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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