Advances in Natural Computing: Methods and Applications

Topic Information

Dear Colleagues,

Natural computing, as a cutting-edge computational paradigm, has made significant progress in both theoretical research and practical applications in recent years. Drawing inspiration from natural phenomena, biological mechanisms, and physicochemical processes, it has developed nature-inspired computational models and meta-heuristic algorithms, providing innovative solutions for complex problems that are challenging for traditional computing methods. These approaches harness principles such as evolution, swarm intelligence, self-organization, and adaptability, enabling breakthroughs in optimization, learning, and system design. Research in natural computing not only advances computer science but also fosters interdisciplinary collaborations with fields like artificial intelligence, bioinformatics, physics, and quantum computing, demonstrating vast potential for cross-domain innovation. We welcome submissions on topics including but not limited to the following: Theoretical foundations of natural computing, including nature-inspired models and the development of novel meta-heuristic algorithms. Applications of natural computing in artificial intelligence (e.g., neural networks, reinforcement learning). Applications in bioinformatics (e.g., sequence analysis, protein structure prediction). Meta-heuristic algorithms for optimization problems in engineering, logistics, and industry. Synergies between natural computing and quantum computing. The modeling and analysis of complex systems using nature-inspired approaches. By integrating nature-inspired principles and meta-heuristic strategies, this Topic aims to highlight advancements that bridge computational theory with real-world challenges. We encourage contributions that explore both foundational innovations and practical implementations.

Prof. Dr. Gaige Wang
Prof. Xiao-Zhi Gao
Dr. Ying Tian
Topic Editors

Keywords

Participating Journals

Journal Name	Impact Factor	CiteScore	Launched Year	First Decision (median)	APC
AI ai	5.0	6.9	2020	19.2 Days	CHF 1800	Submit
Algorithms algorithms	2.1	4.5	2008	19.2 Days	CHF 1800	Submit
Applied Sciences applsci	2.5	5.5	2011	16 Days	CHF 2400	Submit
AppliedMath appliedmath	0.7	1.1	2021	20.6 Days	CHF 1200	Submit
Electronics electronics	2.6	6.1	2012	16.4 Days	CHF 2400	Submit
Mathematics mathematics	2.2	4.6	2013	17.3 Days	CHF 2600	Submit

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All AI Algorithms Applied Sciences Electronics Mathematics AppliedMath

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30 pages, 734 KB  

Open AccessArticle

A Sixth-Order Vieta–Lucas Polynomial-Based Block Method with Optimal Stability for Solving Practical First-Order ODE Models

by Olugbade Ezekiel Faniyi, Mark Ifeanyi Modebei, Matthew Olanrewaju Oluwayemi and Ikechukwu Jackson Otaide

AppliedMath 2026, 6(2), 34; https://doi.org/10.3390/appliedmath6020034 - 13 Feb 2026

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Abstract

This paper addresses the numerical integration of first-order ordinary differential equations by developing a continuous linear multistep block method. The method is constructed through the approximation of the exact solution using a linear combination of shifted Vieta–Lucas polynomials defined on the interval [...] Read more.

This paper addresses the numerical integration of first-order ordinary differential equations by developing a continuous linear multistep block method. The method is constructed through the approximation of the exact solution using a linear combination of shifted Vieta–Lucas polynomials defined on the interval $[0, 4]$. The use of this polynomial basis extends traditional approximation approaches and provides improved stability while maintaining high-order accuracy. Theoretical analysis shows that the proposed method attains sixth-order convergence and possesses an extended stability interval of $[-19.5,0]$, ensuring reliable performance for moderately stiff problems. Numerical experiments confirm that the method achieves lower errors and higher computational efficiency than conventional methods. These results demonstrate the suitability of the proposed approach for scientific computing applications, including engineering simulations and mathematical modeling, where accurate numerical integration of first-order differential equation is required. Full article

(This article belongs to the Topic Advances in Natural Computing: Methods and Applications)

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