Computational and Mathematical Methods最新文献

Acceleration of Volume Integral Equations Using Trimmed Multilevel Fast Multipole Algorithm 基于修剪多层快速多极算法的体积积分方程加速

IF 1.5

Computational and Mathematical Methods Pub Date : 2026-07-31 DOI: 10.1155/cmm4/6460608

Halil Topözlü, Barişcan Karaosmanoğlu, Vakur Behçet Ertürk

{"title":"Acceleration of Volume Integral Equations Using Trimmed Multilevel Fast Multipole Algorithm","authors":"Halil Topözlü, Barişcan Karaosmanoğlu, Vakur Behçet Ertürk","doi":"10.1155/cmm4/6460608","DOIUrl":"10.1155/cmm4/6460608","url":null,"abstract":"The concept of trimmed tree structures for multilevel fast multipole algorithm (MLFMA), referred to as trimmed-MLFMA (T-MLFMA), is proposed for the solution of volume integral equations for the fast analysis of scattering from large, inhomogeneous objects, where the conventional MLFMA suffers from high number of iterations and matrix vector multiplication (MVM) of large matrices at each iteration. In T-MLFMA, thresholding and machine learning techniques are used to eliminate the redundant interactions as the iterations proceed. In particular, the converged basis function coefficients are estimated with a fully connected neural network and, together with the thresholding, the MLFMA tree structure is systematically pruned, and the resulting far-interaction matrix becomes sparser. As a result, both the number of iterations and the MVM time per iteration are dramatically reduced. Using only a group of small homogeneous dielectric spheres with different permittivity values at the training stage, we are able to show that scattering from large, highly inhomogeneous and fairly complex objects are solved accurately and significantly faster than the conventional MLFMA solution (up to 10 times).","PeriodicalId":100308,"journal":{"name":"Computational and Mathematical Methods","volume":"2026 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2026-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1155/cmm4/6460608","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148617331","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Fractional Dynamics of Nonlinear Liquid Dispersion Pattern Drops: A Robust Analytical Study of Modulation Instability and Compacton Structures 非线性液体色散模式滴的分数动力学：调制不稳定性和紧致结构的鲁棒分析研究

IF 1.5

Computational and Mathematical Methods Pub Date : 2026-07-28 DOI: 10.1155/cmm4/2166854

Yogeshwari F. Patel, Mohammad Izadi, Hany M. Ahmed

{"title":"Fractional Dynamics of Nonlinear Liquid Dispersion Pattern Drops: A Robust Analytical Study of Modulation Instability and Compacton Structures","authors":"Yogeshwari F. Patel, Mohammad Izadi, Hany M. Ahmed","doi":"10.1155/cmm4/2166854","DOIUrl":"https://doi.org/10.1155/cmm4/2166854","url":null,"abstract":"Nonlinear dispersion phenomena in liquid media often lead to the formation of localized structures such as compact wave packets and dispersion drops. The present investigation demonstrates that the proposed analytical framework yields accurate approximate solutions, successfully captures compacton-like structures, and clearly reveals the critical influence of the fractional-order parameter on modulation instability and nonlinear wave evolution. In this work, we present a systematic analytical investigation of nonlinear liquid dispersion drops governed by a time-fractional Rosenau–Hyman equation formulated in the notion of the Liouville–Caputo fractional derivative. The fractional framework allows the incorporation of memory effects that significantly influence the evolution of nonlinear dispersive waves. Using an efficient analytical scheme, approximate solutions are constructed and their dynamical behavior is examined for different fractional orders and physical parameters. The obtained results reveal the emergence of localized compacton-like structures that characterize nonlinear liquid dispersion patterns. To further understand the stability of these structures, a detailed modulation instability analysis is performed. The derived instability spectrum identifies the neutral stability boundaries and clarifies the conditions under which small perturbations grow and generate nonlinear wave structures. The systematic investigation demonstrates that the fractional order plays a crucial role in the formation of localized dispersion drops and controlling the instability growth rate. The present study provides new theoretical insights into nonlinear liquid dispersion mechanisms and offers a useful analytical framework for investigating complex wave dynamics in fractional dispersive media.","PeriodicalId":100308,"journal":{"name":"Computational and Mathematical Methods","volume":"2026 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2026-07-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1155/cmm4/2166854","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148616285","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Fractional Dynamics of Nonlinear Liquid Dispersion Pattern Drops: A Robust Analytical Study of Modulation Instability and Compacton Structures 非线性液体色散模式滴的分数动力学：调制不稳定性和紧致结构的鲁棒分析研究

IF 1.5

Computational and Mathematical Methods Pub Date : 2026-07-28 DOI: 10.1155/cmm4/2166854

Yogeshwari F. Patel, Mohammad Izadi, Hany M. Ahmed

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引用次数: 0

Fractional Epidemic Dynamics With Memory: Rigorous Analysis, Data-Constrained Learning, and Physics-Informed Forecasting 具有记忆的部分流行病动力学：严格分析，数据约束学习和物理信息预测

IF 1.5

Computational and Mathematical Methods Pub Date : 2026-07-24 DOI: 10.1155/cmm4/3732177

Younes Brahim Oumedjber, Akram Boukabache, Nadjette Debbouche, Adel Ouannas, Giuseppe Grassi, Ibrahim Alraddadi

引用次数: 0

Fractional Epidemic Dynamics With Memory: Rigorous Analysis, Data-Constrained Learning, and Physics-Informed Forecasting 具有记忆的部分流行病动力学：严格分析，数据约束学习和物理信息预测

IF 1.5

Computational and Mathematical Methods Pub Date : 2026-07-24 DOI: 10.1155/cmm4/3732177

Younes Brahim Oumedjber, Akram Boukabache, Nadjette Debbouche, Adel Ouannas, Giuseppe Grassi, Ibrahim Alraddadi

引用次数: 0

A Novel Fractional Iterative Technique of Order (2λ + 1) With Applications to Engineering 一种新的（2λ + 1）阶分数阶迭代技术及其工程应用

IF 1.5

Computational and Mathematical Methods Pub Date : 2026-06-19 DOI: 10.1155/cmm4/2841446

Saima Akram, Faiza Akram, Mutti-Ur Rehman, Rida Batool, Tursunov Boxodir Junaydullayevich

{"title":"A Novel Fractional Iterative Technique of Order (2λ + 1) With Applications to Engineering","authors":"Saima Akram, Faiza Akram, Mutti-Ur Rehman, Rida Batool, Tursunov Boxodir Junaydullayevich","doi":"10.1155/cmm4/2841446","DOIUrl":"https://doi.org/10.1155/cmm4/2841446","url":null,"abstract":"Fractional derivatives are widely used to model complex phenomena where classical derivatives fail to provide accurate solutions. As a result, iterative methods involving fractional derivatives have become highly significant for addressing such challenges. At present, the literature reports only two existing two-step fractional iterative methods, highlighting a significant gap and emphasizing the need for further advancement in this area of research. In this work, we introduced a novel class of advanced fractional iterative algorithms using Caputo and Riemann-Liouville fractional derivatives designed to enhance the efficiency of solving complex mathematical problems. Our approach presented a two-step iterative method of order (2λ + 1), effectively addressing situations where standard derivatives are insufficient, using fractional derivatives. This technique requires only two functions and one evaluation of the fractional derivative, making it highly efficient. We established the applicability of our method in solving nonlinear equations across diverse scientific disciplines, including chemical sciences, civil engineering, beam support system, corporate logistics, bacterial growth modeling, and bridge beam deflection analysis. Extensive numerical experiments, conducted using Maple 2022, validate the performance of the proposed algorithm, with comparisons based on absolute error and computational efficiency at each iterative step. The results demonstrate that our method outperforms existing techniques, exhibiting significantly reduced absolute errors. Furthermore, graphical error comparisons, generated using MATLAB 2018a, illustrate the superior accuracy and thus may be considered a significant addition to the existing scholarly literature.","PeriodicalId":100308,"journal":{"name":"Computational and Mathematical Methods","volume":"2026 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2026-06-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1155/cmm4/2841446","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148282227","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

A Novel Fractional Iterative Technique of Order (2λ + 1) With Applications to Engineering 一种新的（2λ + 1）阶分数阶迭代技术及其工程应用

IF 1.5

Computational and Mathematical Methods Pub Date : 2026-06-19 DOI: 10.1155/cmm4/2841446

Saima Akram, Faiza Akram, Mutti-Ur Rehman, Rida Batool, Tursunov Boxodir Junaydullayevich

{"title":"A Novel Fractional Iterative Technique of Order (2λ + 1) With Applications to Engineering","authors":"Saima Akram, Faiza Akram, Mutti-Ur Rehman, Rida Batool, Tursunov Boxodir Junaydullayevich","doi":"10.1155/cmm4/2841446","DOIUrl":"https://doi.org/10.1155/cmm4/2841446","url":null,"abstract":"Fractional derivatives are widely used to model complex phenomena where classical derivatives fail to provide accurate solutions. As a result, iterative methods involving fractional derivatives have become highly significant for addressing such challenges. At present, the literature reports only two existing two-step fractional iterative methods, highlighting a significant gap and emphasizing the need for further advancement in this area of research. In this work, we introduced a novel class of advanced fractional iterative algorithms using Caputo and Riemann-Liouville fractional derivatives designed to enhance the efficiency of solving complex mathematical problems. Our approach presented a two-step iterative method of order (2λ + 1), effectively addressing situations where standard derivatives are insufficient, using fractional derivatives. This technique requires only two functions and one evaluation of the fractional derivative, making it highly efficient. We established the applicability of our method in solving nonlinear equations across diverse scientific disciplines, including chemical sciences, civil engineering, beam support system, corporate logistics, bacterial growth modeling, and bridge beam deflection analysis. Extensive numerical experiments, conducted using Maple 2022, validate the performance of the proposed algorithm, with comparisons based on absolute error and computational efficiency at each iterative step. The results demonstrate that our method outperforms existing techniques, exhibiting significantly reduced absolute errors. Furthermore, graphical error comparisons, generated using MATLAB 2018a, illustrate the superior accuracy and thus may be considered a significant addition to the existing scholarly literature.","PeriodicalId":100308,"journal":{"name":"Computational and Mathematical Methods","volume":"2026 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2026-06-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1155/cmm4/2841446","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148282220","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Analysis and Validation of a Real-Time AR-IoT Training System via Nonlinear Dynamical Modeling 基于非线性动力学建模的实时AR-IoT训练系统分析与验证

IF 1.5

Computational and Mathematical Methods Pub Date : 2026-06-18 DOI: 10.1155/cmm4/1316357

Thittaporn Ganokratanaa, Mahasak Ketcham, Patiyuth Pramkeaw

{"title":"Analysis and Validation of a Real-Time AR-IoT Training System via Nonlinear Dynamical Modeling","authors":"Thittaporn Ganokratanaa, Mahasak Ketcham, Patiyuth Pramkeaw","doi":"10.1155/cmm4/1316357","DOIUrl":"https://doi.org/10.1155/cmm4/1316357","url":null,"abstract":"This paper presents a formally validated real-time AR-IoT firearm training framework, in which classical control-theoretic tools are embedded as a system-level validation layer rather than as novel theoretical contributions. Unlike prior AR-based training systems that rely primarily on heuristic or empirical design, the proposed framework introduces a mathematically grounded structure that explicitly accounts for user interactions, synchronization delays, and energy constraints encountered in real-world deployment. The system is modeled using discrete-time dynamical equations under bounded disturbances, and five theoretical assumptions related to state boundedness, delay tolerance, and energy consumption are formalized. Classical stability and input-to-state stability (ISS) concepts are employed to provide an analysis-based validation of boundedness, synchronization accuracy, and robustness, serving as a formal certification mechanism for the training system. A set of standard analytical results (recalling classical nonlinear stability/ISS tools) is used and supported by numerical experiments under diverse conditions, including sensor noise and delayed inputs. The theoretical framework is further implemented in a practical AR-IoT firearm training prototype that integrates marker-based AR overlays, Bluetooth-enabled microcontrollers, and IPSC-compliant scoring mechanisms. Real-time data from laser-triggered events, motion sensors, and visual feedback are processed to deliver adaptive scoring and trainee guidance. Experimental results demonstrate that the system consistently converges to stable feedback patterns while maintaining low-latency performance under dynamic conditions. Overall, this work contributes a system-level integration of mathematical validation and real-time deployment, offering a scalable and verifiably reliable solution for immersive firearm training in safety-critical environments.","PeriodicalId":100308,"journal":{"name":"Computational and Mathematical Methods","volume":"2026 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2026-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1155/cmm4/1316357","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148282392","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Analysis and Validation of a Real-Time AR-IoT Training System via Nonlinear Dynamical Modeling 基于非线性动力学建模的实时AR-IoT训练系统分析与验证

IF 1.5

Computational and Mathematical Methods Pub Date : 2026-06-18 DOI: 10.1155/cmm4/1316357

Thittaporn Ganokratanaa, Mahasak Ketcham, Patiyuth Pramkeaw

{"title":"Analysis and Validation of a Real-Time AR-IoT Training System via Nonlinear Dynamical Modeling","authors":"Thittaporn Ganokratanaa, Mahasak Ketcham, Patiyuth Pramkeaw","doi":"10.1155/cmm4/1316357","DOIUrl":"https://doi.org/10.1155/cmm4/1316357","url":null,"abstract":"This paper presents a formally validated real-time AR-IoT firearm training framework, in which classical control-theoretic tools are embedded as a system-level validation layer rather than as novel theoretical contributions. Unlike prior AR-based training systems that rely primarily on heuristic or empirical design, the proposed framework introduces a mathematically grounded structure that explicitly accounts for user interactions, synchronization delays, and energy constraints encountered in real-world deployment. The system is modeled using discrete-time dynamical equations under bounded disturbances, and five theoretical assumptions related to state boundedness, delay tolerance, and energy consumption are formalized. Classical stability and input-to-state stability (ISS) concepts are employed to provide an analysis-based validation of boundedness, synchronization accuracy, and robustness, serving as a formal certification mechanism for the training system. A set of standard analytical results (recalling classical nonlinear stability/ISS tools) is used and supported by numerical experiments under diverse conditions, including sensor noise and delayed inputs. The theoretical framework is further implemented in a practical AR-IoT firearm training prototype that integrates marker-based AR overlays, Bluetooth-enabled microcontrollers, and IPSC-compliant scoring mechanisms. Real-time data from laser-triggered events, motion sensors, and visual feedback are processed to deliver adaptive scoring and trainee guidance. Experimental results demonstrate that the system consistently converges to stable feedback patterns while maintaining low-latency performance under dynamic conditions. Overall, this work contributes a system-level integration of mathematical validation and real-time deployment, offering a scalable and verifiably reliable solution for immersive firearm training in safety-critical environments.","PeriodicalId":100308,"journal":{"name":"Computational and Mathematical Methods","volume":"2026 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2026-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1155/cmm4/1316357","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148282391","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

On Efficient Iterative Algorithms and Conditioning for the Nonlinear Sylvester Equation 非线性Sylvester方程的有效迭代算法与条件

IF 1.5

Computational and Mathematical Methods Pub Date : 2026-06-17 DOI: 10.1155/cmm4/9773355

Constantino Mahinya, Chacha Stephen Chacha

{"title":"On Efficient Iterative Algorithms and Conditioning for the Nonlinear Sylvester Equation","authors":"Constantino Mahinya, Chacha Stephen Chacha","doi":"10.1155/cmm4/9773355","DOIUrl":"https://doi.org/10.1155/cmm4/9773355","url":null,"abstract":"Nonlinear Sylvester-type matrix equations arise in applications such as control theory, observer design, model reduction, and data-driven systems, where they model higher order interactions in matrix transformations. Unlike the classical Sylvester equation, the presence of nonlinear terms introduces additional analytical challenges and increased numerical complexity, particularly for large-scale problems. This work explores a nonlinear Sylvester equation with a polynomial matrix power and develops Newton-based iterative methods tailored to its structure. These include the classical Newton method, line-search stabilized variants, an overrelaxed (OSOR) scheme, and a matrix-free Newton–Krylov approach exploiting structured matrix–vector products. We also present a conditioning and sensitivity analysis based on Fréchet derivatives, yielding explicit normwise, mixed, and componentwise condition numbers and corresponding perturbation bounds. Numerical experiments demonstrate the effectiveness of stabilization and matrix-free techniques, particularly for ill-conditioned or strongly nonlinear problems.","PeriodicalId":100308,"journal":{"name":"Computational and Mathematical Methods","volume":"2026 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2026-06-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1155/cmm4/9773355","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148282236","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0