A high-efficiency fourth-order iterative method for nonlinear equations: Convergence and computational gains

IF 1.8 2区数学 Q1 MATHEMATICS

Journal of Complexity Pub Date : 2025-09-23 DOI:10.1016/j.jco.2025.101994

Amir Naseem , Krzysztof Gdawiec , Sania Qureshi , Ioannis K. Argyros , Muhammad Aziz ur Rehman , Amanullah Soomro , Evren Hincal , Kamyar Hosseini , Ausif Padder

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引用次数: 0

Abstract

This study introduces an optimal fourth-order iterative method derived by combining two established methods, resulting in enhanced convergence when solving nonlinear equations. Through rigorous convergence analysis using both Taylor expansion and the Banach space framework, the fourth-order optimality condition is verified. We demonstrate the superior efficiency and stability of this new method compared to traditional alternatives. Numerical experiments confirm its effectiveness, showing a reduction in the average number of iterations and computational time. Visual analysis with polynomiographs confirms the method's robustness, focusing on convergence area index, iteration count, computational time, fractal dimension, and Wada measure of basins. These findings underscore the potential of this optimal method for tackling complex nonlinear problems in various scientific and engineering fields.

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非线性方程的高效四阶迭代法：收敛性与计算增益

本文引入了一种将两种已有方法结合起来的四阶最优迭代方法，从而提高了求解非线性方程的收敛性。通过Taylor展开式和Banach空间框架的严格收敛分析，验证了四阶最优性条件。与传统方法相比，我们证明了这种新方法的效率和稳定性。数值实验证实了该方法的有效性，表明该方法减少了平均迭代次数和计算时间。在收敛面积指数、迭代次数、计算时间、分形维数和Wada测度等方面，通过多项式图的可视化分析证实了该方法的鲁棒性。这些发现强调了这种解决各种科学和工程领域复杂非线性问题的最佳方法的潜力。

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

Journal of Complexity 工程技术-计算机：理论方法

CiteScore

3.10

自引率

17.60%

发文量

审稿时长

>12 weeks

期刊介绍： The multidisciplinary Journal of Complexity publishes original research papers that contain substantial mathematical results on complexity as broadly conceived. Outstanding review papers will also be published. In the area of computational complexity, the focus is on complexity over the reals, with the emphasis on lower bounds and optimal algorithms. The Journal of Complexity also publishes articles that provide major new algorithms or make important progress on upper bounds. Other models of computation, such as the Turing machine model, are also of interest. Computational complexity results in a wide variety of areas are solicited. Areas Include: • Approximation theory • Biomedical computing • Compressed computing and sensing • Computational finance • Computational number theory • Computational stochastics • Control theory • Cryptography • Design of experiments • Differential equations • Discrete problems • Distributed and parallel computation • High and infinite-dimensional problems • Information-based complexity • Inverse and ill-posed problems • Machine learning • Markov chain Monte Carlo • Monte Carlo and quasi-Monte Carlo • Multivariate integration and approximation • Noisy data • Nonlinear and algebraic equations • Numerical analysis • Operator equations • Optimization • Quantum computing • Scientific computation • Tractability of multivariate problems • Vision and image understanding.