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

IF 4.6 Q2 MATERIALS SCIENCE, BIOMATERIALS
Ramandeep Behl, Ioannis K. Argyros, Sattam Alharbi
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引用次数: 0

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.
加快高阶方程求解方法的收敛速度
本文介绍了一种多步骤方法,用于开发求解巴拿赫空间值方程的序列。它提供了误差估计、收敛半径和唯一性结果。我们的方法提高了推荐方法的适用性,并解决了应用科学中的难题。理论上的进步得到了全面计算结果的支持,证明了早期方法的实际适用性和稳健性。我们为所考虑的方法提供了可计算的误差估计和明确的收敛半径,从而确保巴拿赫空间值方程的解更加可靠和精确。我们的结论是,我们的工作极大地改进了多步方法的实用性,为解决巴拿赫空间中的复杂方程提供了一种严格的可计算方法,并具有强大的理论和计算结果。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
ACS Applied Bio Materials
ACS Applied Bio Materials Chemistry-Chemistry (all)
CiteScore
9.40
自引率
2.10%
发文量
464
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