Accelerating the Speed of Convergence for High-Order Methods to Solve Equations

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 17, 1-22

Abstract: This article introduces a multistep method for developing sequences that solve Banach space-valued equations. It provides error estimates, a radius of convergence, and uniqueness results. Our approach improves the applicability of the recommended method and addresses challenges in applied science. The theoretical advancements are supported by comprehensive computational results, demonstrating the practical applicability and robustness of the earlier method. We ensure more reliable and precise solutions to Banach space-valued equations by providing computable error estimates and a clear radius of convergence for the considered method. We conclude that our work significantly improves the practical utility of multistep methods, offering a rigorous and computable approach to solving complex equations in Banach spaces, with strong theoretical and computational results.

Keywords: multistep method; ball convergence; generalized continuity; Banach space (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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