Mathematics and Computers in Simulation最新文献

{"title":"Combinatorial potential of random equations with mixture models: Modeling and simulation","authors":"Wolfgang Hoegele","doi":"10.1016/j.matcom.2025.07.033","DOIUrl":"10.1016/j.matcom.2025.07.033","url":null,"abstract":"<div><div>The goal of this paper is to demonstrate the general modeling and practical simulation of random equations with mixture model parameter random variables. Random equations, understood as stationary (non-dynamical) equations with parameters as random variables, have a long history and a broad range of applications. The specific novelty of this explorative study lies on the demonstration of the combinatorial complexity of these equations and their solutions with mixture model parameters. In a Bayesian argumentation framework, we derive a likelihood function and posterior density of approximate solutions while avoiding significant restrictions about the type of nonlinearity of the equation or mixture models, and demonstrate their numerically efficient implementation for the applied researcher. In the results section, we are specifically focusing on expressive example simulations showcasing the combinatorial potential of random linear equation systems and nonlinear systems of random conic section equations. Introductory applications to portfolio optimization, stochastic control and random matrix theory are provided in order to show the wide applicability of the presented methodology.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"239 ","pages":"Pages 696-715"},"PeriodicalIF":4.4,"publicationDate":"2025-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144722580","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Advanced heuristic computing with Gudermannian neural networks for mathematical modeling of divorced dynamics in social networks","authors":"Sana Ullah Saqib ,&nbsp;Yin-Tzer Shih ,&nbsp;Muhammad Wajahat Anjum ,&nbsp;Muhammad Shoaib","doi":"10.1016/j.matcom.2025.07.048","DOIUrl":"10.1016/j.matcom.2025.07.048","url":null,"abstract":"<div><div>This study investigates the transmission dynamics of divorce within social networks through the innovative application of Gudermannian neural networks (GNNs), combined with a hybrid optimization framework that integrates heuristic genetic algorithms (HGAs) and sequential quadratic programming (SQP). The proposed methodology, referred to as HGA-SQP-GNN, is employed to analyze the intricacies of marital dissolution, encapsulated within the Married-Divorced-Separated (MDS) mathematical framework. This framework categorizes individuals into three distinct groups: Married (M), Divorced (D), and Separated (S). The findings show that about 80 % of marriages end in separation by the end of the observed period. This statistic highlights how divorced individuals can significantly influence the likelihood of separation among married couples, emphasizing the need for targeted interventions to address the rise of broken families. Furthermore, the study demonstrates the robustness and effectiveness of the proposed HGA-SQP-GNN algorithm, as shown by the optimal solutions achieved compared to the traditional Adam method. Our study highlights the urgent need for focused interventions to curb the proliferation of broken families. A hybrid technique, HGA-SQP-GNN, enables rapid convergence optimization by minimizing the mean square error (MSE), which acts as the fitness function for optimization. The robustness and efficacy of the proposed algorithm are confirmed by comparing the optimal solutions of the hybrid approach with the numerical results obtained from the Adam method. The precise measurements of absolute error findings, ranging from 10⁻² to 10⁻¹², demonstrate the value and effectiveness of the proposed algorithm. The reliability, stability, and convergence characteristics of the integrated techniques are further verified through statistical analyses, including mean absolute deviation, root mean square error, and Theil's inequality coefficient. Additionally, the lower values of minimum, median, and SIR, ranging from 10⁻⁵ to 10⁻¹², further validate the accuracy, robustness, and efficacy of the proposed solver.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"239 ","pages":"Pages 745-765"},"PeriodicalIF":4.4,"publicationDate":"2025-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144748992","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"PID tuning strategies for boost converters. Optimal compromise between performance and noise amplification","authors":"Roberto Sanchis ,&nbsp;José María Martín","doi":"10.1016/j.matcom.2025.07.009","DOIUrl":"10.1016/j.matcom.2025.07.009","url":null,"abstract":"<div><div>This paper presents some PID tuning strategies for the control of boost converters, that exhibit non-minimum phase behavior. First, some simple model identification techniques based on the step response are presented. Then, a PID tuning technique based on the fixed robustness tuning line concept, developed by the authors, is revised and applied to the tuning of PID controllers for boost converters. The proposed techniques allow the user to freely select the desired robustness, defined as the maximum sensitivity (<span><math><msub><mrow><mi>M</mi></mrow><mrow><mi>s</mi></mrow></msub></math></span>). They also permit to find an optimal compromise between measurement noise amplification and performance, in terms of disturbance rejection and reference tracking. Some direct tuning equations are also proposed to directly compute the controller parameters using some measurements from an open-loop step test. No previous proposals in literature about PID tuning of boost converters allow the free selection of robustness and compromise between performance and noise amplification, as the proposed approach. Experimental validation on two real boost converter prototypes, one overdamped and one underdamped, show the superiority of the proposed approaches, measured in terms of robustness, disturbance IAE, settling time and overshoot in the step response, compared to the use of a theoretical model of the converter based on the component values. The experiments demonstrate a reduction in the overshoot from 50% to less than 5%, and a 30% reduction in the settling time compared to theoretical model-based tuning. The results of this paper are intended for those practitioners who design boost converters and want a simple tool to tune the PID controller for the converter.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"240 ","pages":"Pages 381-402"},"PeriodicalIF":4.4,"publicationDate":"2025-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144712867","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Stability analysis of fractional-order cone-invariant systems with distributed delays","authors":"Zhiye Bai ,&nbsp;Baowei Wu ,&nbsp;Yue-E Wang ,&nbsp;Hongling Qiu","doi":"10.1016/j.matcom.2025.07.016","DOIUrl":"10.1016/j.matcom.2025.07.016","url":null,"abstract":"<div><div>This article addresses the problem of stability and gain analysis for fractional-order cone-invariant systems subjected to time-varying distributed delays. Depending on the Banach fixed point theorem, the system’s solution is demonstrated to exist uniquely. Subsequently, a necessary and sufficient criterion is deduced to guarantee the cone invariance of delayed systems using a fractional differential operator. By combining the partial order relation on proper cones with the inductive reasoning, the asymptotic stability of fractional-order cone-preserving systems with distributed delays is demonstrated, with stability conditions that are equivalent to those of systems with constant delays. Furthermore, an explicit representation of cone-induced gain is put forward for cone-invariant systems in the presence of delays via utilizing the comparison principle, revealing that the cone-induced gain depends on the duration of the distributed delays. Finally, numerical simulations are performed to verify the rationality of the obtained results.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"240 ","pages":"Pages 558-570"},"PeriodicalIF":4.4,"publicationDate":"2025-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144749348","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Mathematical and computational analysis of a fractional-order drug abuse model with nonlinear incidence and logistic growth","authors":"Mohammad Izadi ,&nbsp;Pundikala Veeresha ,&nbsp;Waleed Adel","doi":"10.1016/j.matcom.2025.07.032","DOIUrl":"10.1016/j.matcom.2025.07.032","url":null,"abstract":"<div><div>This paper presents a novel mathematical model for analyzing the dynamics of drug addiction using a fractional-order system based on the Liouville–Caputo derivative. The proposed model incorporates a nonlinear saturated incidence rate, logistic growth in the addiction compartments, and seven interconnected subpopulations representing different stages of drug use and recovery, including relapse and awareness. We conduct a rigorous mathematical analysis to establish the existence, uniqueness, positivity, and boundedness of solutions, ensuring the epidemiological and physical validity of the model. The basic reproduction number <span><math><msub><mrow><mi>R</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span> is derived, and the local and global stability of the equilibrium points is analyzed. A major contribution of this work is the application of a new domain decomposition spectral method based on second-kind Dickson polynomials, combined with the quasilinearization technique, to efficiently solve the complex nonlinear system. The convergence of the numerical method is theoretically validated. Numerical simulations are provided to illustrate the model’s dynamics and to explore the impact of various parameters and intervention strategies. Compared to existing models, this study offers an improved framework for understanding memory-dependent behavior in addiction dynamics and introduces a computationally efficient approach to solve fractional-order systems with high accuracy.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"240 ","pages":"Pages 451-472"},"PeriodicalIF":4.4,"publicationDate":"2025-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144714453","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A modified Riemannian hybrid conjugate gradient method for nonconvex optimization problems","authors":"Yun Wang,&nbsp;Yicong Bian,&nbsp;Hu Shao","doi":"10.1016/j.matcom.2025.07.026","DOIUrl":"10.1016/j.matcom.2025.07.026","url":null,"abstract":"<div><div>This paper proposes a new Riemannian hybrid conjugate gradient method aimed at solving nonconvex optimization problems on Riemannian manifolds. We extend the modified PRP and HS methods (WYL and VHS methods) to Riemannian manifolds, and introduce a new hybrid parameter that ensures the search direction always satisfies the descent property without requiring any line search. The global convergence of the method is established under the Riemannian weak Wolfe conditions. Finally, through numerical comparison with existing Riemannian conjugate gradient methods on five test problems, we validate the effectiveness of the proposed method.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"239 ","pages":"Pages 679-695"},"PeriodicalIF":4.4,"publicationDate":"2025-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144722571","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Application of χ-fractional Genocchi wavelets for solving χ-fractional differential equations","authors":"Parisa Rahimkhani ,&nbsp;Thabet Abdeljawad","doi":"10.1016/j.matcom.2025.07.031","DOIUrl":"10.1016/j.matcom.2025.07.031","url":null,"abstract":"<div><div>This paper proposes an efficient approximation technique to solve <span><math><mi>χ</mi></math></span>-fractional differential equations, and <span><math><mi>χ</mi></math></span>-fractional delay differential equations. The method relies on utilizing a new type of functions called the <span><math><mi>χ</mi></math></span>-fractional Genocchi wavelets. The characteristics of <span><math><mi>χ</mi></math></span>-fractional Genocchi wavelets basis functions are provided and illustrated. An exact formula, employing the regularized beta function, is presented for computing the <span><math><mrow><mi>χ</mi><mo>−</mo></mrow></math></span>Riemann–Liouville fractional integral operator of these functions. This formula, the provided wavelets, and the collocation method are employed to find the solutions of <span><math><mi>χ</mi></math></span>-fractional differential equations, and <span><math><mi>χ</mi></math></span>-fractional delay differential equations. The method’s convergence is rigorously justified. Finally, three numerical examples are presented to illustrate the efficiency and precision of this method.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"239 ","pages":"Pages 790-804"},"PeriodicalIF":4.4,"publicationDate":"2025-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144772688","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A new second-order accurate Strang splitting type exponential integrator for semilinear parabolic problems","authors":"Saburi Rasheed ,&nbsp;Olaniyi S. Iyiola ,&nbsp;Bruce A. Wade","doi":"10.1016/j.matcom.2025.07.028","DOIUrl":"10.1016/j.matcom.2025.07.028","url":null,"abstract":"<div><div>A novel exponential integrator is developed to address two-dimensional semilinear parabolic problems with both smooth and non-smooth boundary and initial conditions. This integrator is characterized by its computational efficiency, L-stability, parallelizability, and second-order accuracy. This method employs a rational function (non-Padé type), specifically, the real distinct pole (RDP), to estimate the matrix exponentials involved in the integration scheme. This novel Strang-splitting-type exponential time differencing (ETD) scheme is utilized to address various reaction–diffusion equations (RDEs) under homogeneous Dirichlet, Neumann, and periodic boundary conditions. The experimental results validate and confirm that the proposed exponential integrator is of second-order convergence rate. The examples provided demonstrate the superior accuracy and efficiency of this technique compared with existing second-order methods.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"240 ","pages":"Pages 538-557"},"PeriodicalIF":4.4,"publicationDate":"2025-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144739287","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Fixed-time synchronization of fractional-order Hopfield neural networks with proportional delays","authors":"Pushpendra Kumar ,&nbsp;El Abed Assali","doi":"10.1016/j.matcom.2025.07.035","DOIUrl":"10.1016/j.matcom.2025.07.035","url":null,"abstract":"<div><div>This article explores the fixed-time synchronization of fractional-order Hopfield neural networks incorporating proportional delays. Unlike finite-time synchronization, where the convergence time varies based on the initial synchronization errors, fixed-time synchronization allows for a predetermined settling time that remains independent of initial conditions. To achieve fixed-time synchronization, two types of feedback control strategies incorporating fractional integrals are employed: one based on state feedback and another utilizing a controller designed with a Lyapunov function and an exponential function. By designing appropriate Lyapunov functions and employing inequality techniques, multiple sufficient conditions were established to guarantee the fixed-time synchronization of the considered systems under these control strategies. Finally, two numerical examples are presented to demonstrate the validity and practical relevance of the theoretical findings.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"240 ","pages":"Pages 367-380"},"PeriodicalIF":4.4,"publicationDate":"2025-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144702782","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A high accurate numerical framework for the solution of the vanishing-delay Volterra integro-differential equations via Legendre pseudo-spectral element approach","authors":"Yin Yang ,&nbsp;Pai Yao ,&nbsp;Emran Tohidi","doi":"10.1016/j.matcom.2025.07.030","DOIUrl":"10.1016/j.matcom.2025.07.030","url":null,"abstract":"<div><div>In this study, we present a robust numerical framework for solving vanishing-delay Volterra integro-differential equations (VDVIDEs) using the Legendre pseudo-spectral element approach. Our first motivation stems from the limitations of traditional methods such as Runge–Kutta schemes when applied to linear vanishing-delay models. Building upon the robustness of pseudo-spectral element approaches, we extend the application to VDVIDEs and introduce a multi-step Legendre pseudo-spectral Galerkin method (MSLPSGM) to overcome issues related to long computational intervals and high oscillatory solutions. Our suggested approach provides upper bounds for estimating both the solution and its derivative, demonstrating a spectral rate of convergence as the length of sub-intervals decreases and the degree of approximations increases. Extensive numerical examples showcase the robustness and precision of the MSLPSGM in handling VDVIDEs with steep gradients and large computational intervals. The framework’s ability to maintain accuracy across various challenging scenarios underscores its potential as a powerful tool for solving complex integro-differential equations.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"240 ","pages":"Pages 403-422"},"PeriodicalIF":4.4,"publicationDate":"2025-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144712866","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}