Extended Efficient Multistep Solvers for Solving Equations in Banach Spaces

Ramandeep Behl (), Ioannis K. Argyros and Sattam Alharbi
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Ramandeep Behl: Mathematical Modelling and Applied Computation Research Group (MMAC), Department of Mathematics, King Abdulaziz University, Jeddah 21589, Saudi Arabia
Ioannis K. Argyros: Department of Computing and Mathematical Sciences, Cameron University, Lawton, OK 73505, USA
Sattam Alharbi: Department of Mathematics, College of Science and Humanities in Al-Kharj, Prince Sattam Bin Abdulaziz University, Al-Kharj 11942, Saudi Arabia

Mathematics, 2024, vol. 12, issue 12, 1-18

Abstract: In this paper, we investigate the local and semilocal convergence of an iterative method for solving nonlinear systems of equations. We first establish the conditions under which these methods converge locally to the solution. Then, we extend our analysis to examine the semilocal convergence of these methods, considering their behavior when starting from initial guesses that are not necessarily close to the solution. Iterative approaches for solving nonlinear systems of equations must take into account the radius of convergence, computable upper error bounds, and the uniqueness of solutions. These points have not been addressed in earlier studies. Moreover, we provide numerical examples to demonstrate the theoretical findings and compare the performance of these methods under different circumstances. Finally, we conclude that our examination offers a significant understanding of the convergence characteristics of previous iterative techniques for solving nonlinear equation systems.

Keywords: multi-step solver; nonlinear systems; Banach space; convergence order; Lipschitz condition (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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