An accelerated neural dynamics model for solving dynamic nonlinear optimization problem and its applications

Fu, Dongyang; Si, Yang; Wang, Difeng; Xiong, Yizhen

doi:10.1016/j.chaos.2024.114542

Cited by 1 publication

(1 citation statement)

References 33 publications

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“…From the microscopic world of quantum mechanics to the macroscopic scale of climate modeling, nonlinear equations serve as the foundation for capturing the dynamic and non-trivial relationships that characterize the behavior of materials, physical processes, and complex systems. Their application extends to optimization problems [8], signal processing [9], and the modeling of population dynamics [10], emphasizing their pervasive role in advancing our understanding and facilitating the design and optimization of systems in science and engineering [11,12]. In essence, the importance of nonlinear equations lies in their ability to bridge the gap between theoretical models and the intricate realities of the natural and engineered world, providing a powerful tool for analysis, simulation, and innovation.…”

Section: Consider Nonlinear Polynomial Equation Of Degreementioning

confidence: 99%

A New Approach to Multiroot Vectorial Problems: Highly Efficient Parallel Computing Schemes

Shams,

Rafiq,

Carpentieri

et al. 2024

Fractal Fract

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In this article, we construct an efficient family of simultaneous methods for finding all the distinct as well as multiple roots of polynomial equations. Convergence analysis proves that the order of convergence of newly constructed family of simultaneous methods is seventeen. Fractal-based simultaneous iterative algorithms are thoroughly examined. Using self-similar features, fractal-based simultaneous schemes can converge to solutions faster, saving computational time and resources necessary for solving nonlinear equations. Fractals analysis illustrates the newly developed method’s global convergence behavior when compared to single root-finding procedures for solving fractional order polynomials that arise in complex engineering applications. Some real problems from various branches of engineering along with some higher degree polynomials are considered as test examples to show the global convergence property of simultaneous methods, performance and efficiency of the proposed family of methods. Further computational efficiencies, CPU time and residual graphs are also drawn to validate the efficiency, robustness of the newly introduced family of methods as compared to the existing methods in the literature.

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