Mathematics and Computers in Simulation最新文献

{"title":"An optimal and efficient framework for the construction of nonlinear components based on a polynomial ring","authors":"Ch Muhammad Afaq Aslam ,&nbsp;Ikram Ullah ,&nbsp;Muhammad Ishaq","doi":"10.1016/j.matcom.2025.04.022","DOIUrl":"10.1016/j.matcom.2025.04.022","url":null,"abstract":"<div><div>The widespread use of internet makes it essential to protect the private data from the intruders via developing highly secure cryptographic systems. The Substitution box (s-box) is the only nonlinear component of any security system. It plays a crucial role in securing data from an unauthorized access by inverting it into an unreadable form. The algebraic structures are mostly utilized to develop two types of s-box generators, namely the randomized and the optimal generators. The one type outputs dynamic, while the other one is responsible to design s-boxes with high cryptographic properties. However, the generator which gives highly dynamic and optimal s-boxes needs high computational overhead, which limits the encryption throughput of a large useful data set. This fact implies the need of developing an s-box generator that is capable to construct an s-box with high cryptographic properties at a low computational cost. This study presents an innovative algebraic method for constructing optimal s-boxes using a finite field and a polynomial ring. Our approach offers flexibility in selecting unconstrained primes and polynomials, allowing the generation of highly dynamic and nonlinear s-boxes. By evaluating polynomials over a finite field and introducing a new total ordering, we effectively diffuse input elements and derive optimal s-boxes with a nonlinearity of 112. We determine the total number of s-boxes based on the proposed scheme. The performance of the proposed s-box is assessed using standard metrics. We compare the attained results with that of the s-boxes constructed by the recent and state of the art algorithms. Apart from this, we compare the proposed s-box generator with an efficient one regarding the execution time and other cryptographic properties. We showed that the proposed scheme attains the highly nonlinear component approximately 5 times faster than the existing one, and the experimental results indicate that the current method outperforms than others across the standard cryptographic metrics.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"237 ","pages":"Pages 263-280"},"PeriodicalIF":4.4,"publicationDate":"2025-05-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143924063","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 novel BDF-spectral method and its error analysis for Cahn–Hilliard equation in polar geometry","authors":"Jihui Zheng,&nbsp;Zhenlan Pan,&nbsp;Jing An","doi":"10.1016/j.matcom.2025.04.023","DOIUrl":"10.1016/j.matcom.2025.04.023","url":null,"abstract":"<div><div>In this paper, we first propose and study a finite difference Legendre-Fourier spectral method for solving the Cahn–Hilliard equation in polar geometry. The fundamental idea is to restate the original problem in an equivalent form under polar coordinates. Subsequently, by introducing an auxiliary second-order equation, we transform it into a coupled second-order nonlinear system. Furthermore, we introduce a class of weighted Sobolev spaces and their approximation spaces, formulate first- and second-order semi-implicit schemes for the coupled second-order nonlinear system, and demonstrate the stability of these schemes under specific conditions on the time step. In particular, the introduction of pole singularities and the nonlinearity of coupling problem pose significant challenges to theoretical analysis. To overcome these difficulties, we construct a new class of projection operators and prove their approximation properties, thereby providing error estimates for the approximate solutions. Finally, we provide numerous numerical examples, and the numerical results confirm the effectiveness of the algorithm and the correctness of the theoretical findings.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"237 ","pages":"Pages 145-166"},"PeriodicalIF":4.4,"publicationDate":"2025-05-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143906034","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":"Enriched physics-informed neural networks for dynamic Poisson-Nernst-Planck systems","authors":"Xujia Huang ,&nbsp;Fajie Wang ,&nbsp;Benrong Zhang ,&nbsp;Hanqing Liu","doi":"10.1016/j.matcom.2025.04.037","DOIUrl":"10.1016/j.matcom.2025.04.037","url":null,"abstract":"<div><div>This paper proposes a meshless deep learning algorithm, called enriched physics-informed neural networks (EPINNs), to solve dynamic Poisson-Nernst-Planck (PNP) equations characterized by strong coupling and nonlinear behaviors. EPINNs build upon traditional physics-informed neural networks (PINNs) by incorporating an adaptive loss weight mechanism, which automatically adjusts the weights of the loss functions during training, based on maximum likelihood estimation, to achieve balanced optimization. Additionally, a resampling strategy is introduced to accelerate the convergence of the loss function. Four numerical examples are presented to demonstrate the validity and effectiveness of the proposed method. The results show that EPINNs have better applicability than traditional numerical methods in solving such coupled nonlinear systems. Furthermore, EPINNs outperform traditional PINNs in terms of accuracy, stability, and speed. This work provides a robust and efficient numerical tool for solving PNP equations with arbitrary boundary shapes and conditions.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"237 ","pages":"Pages 231-246"},"PeriodicalIF":4.4,"publicationDate":"2025-05-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143918094","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 novel time-fractional decomposition model for image denoising integrating Caputo derivative","authors":"Z. Zaabouli,&nbsp;L. Afraites,&nbsp;A. Laghrib","doi":"10.1016/j.matcom.2025.04.013","DOIUrl":"10.1016/j.matcom.2025.04.013","url":null,"abstract":"<div><div>In this work, we tackle the persistent problem of image restoration by developing a novel model that integrates a Caputo time fractional derivative into a reaction–diffusion framework. This approach exploits the memory effect of fractional derivatives for better diffusion control. With a thorough analysis employing the <em>H^-1</em> norm decomposition strategy and the Weickert filter, our model excels in noise reduction and image quality preservation. The task of establishing solution existence and uniqueness was managed using the fixed point method. The results reveal substantial improvements in denoising performance, highlighting the model’s potential.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"237 ","pages":"Pages 1-17"},"PeriodicalIF":4.4,"publicationDate":"2025-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143903952","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":"On the computational modeling of the behavior of a three-dimensional Brusselator system using a localized meshless method","authors":"Manzoor Hussain ,&nbsp;Abdul Ghafoor","doi":"10.1016/j.matcom.2025.04.020","DOIUrl":"10.1016/j.matcom.2025.04.020","url":null,"abstract":"<div><div>Nonlinear coupled reaction–diffusion equations form an important class of partial differential equations (PDEs) as they are central to the study of certain processes arising in chemical kinetics and biochemical reactions. The analytical solutions of such equations are difficult to establish and often require certain simplified assumptions, which demand for alternative solution procedures. Finite difference, finite element and spectral schemes are well-established methods to tackle such equations, yet they have the challenging issues of mesh generation, underlying integral evaluations, ill-conditioned dense system matrices, and are often restricted by domain geometry. This article presents an efficient and simple localized meshless approximation scheme to analyze the solution behavior of a three-dimensional reaction–diffusion system. The proposed scheme produces sparse (collocation) differentiation matrices for discretization of spatial differential operators which alleviates the problem of ill-conditioned and dense collocation matrices. The scheme is a truly meshless, background integration-free scheme and is equally effective for solving problems over non-rectangular domains with scattered data points. The convergence, stability, and positivity properties of the proposed scheme are theoretically established and numerically verified on some benchmark problems. The outcomes verify the reliability, accuracy, and simplicity of the proposed scheme in higher dimensions when compared to the available results in the literature.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"237 ","pages":"Pages 18-41"},"PeriodicalIF":4.4,"publicationDate":"2025-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143906035","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":"Impact of COVID-19 lockdown in short-term load forecasting","authors":"Miguel López,&nbsp;Sergio Valero,&nbsp;Carolina Senabre","doi":"10.1016/j.matcom.2025.04.035","DOIUrl":"10.1016/j.matcom.2025.04.035","url":null,"abstract":"<div><div>Accurate prediction of electrical demand is crucial for the efficient operation of power systems. However, the unprecedented activity restrictions imposed during the pandemic led to unforeseen disruptions in electrical consumption, challenging the predictive capabilities of existing systems. This phenomenon was widespread, affecting power systems globally, as evidenced by analyses of the Spanish electricity grid presented in this paper. The precision of prediction systems significantly diminished upon the implementation of activity restrictions. This article offers an in-depth analysis of the impact on prediction accuracy in the Spanish context. Moreover, it proposes a method to identify situations where the prediction system is out of control, necessitating corrective measures. The paper introduces a straightforward corrective measure that reduces errors during out-of-control periods. It is designed as an addition to the existing forecast model, modifying its output when an out-of-control situation is reached. The results suggest that further investigation could substantially mitigate the impact of such events and enhance prediction system resilience.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"237 ","pages":"Pages 344-354"},"PeriodicalIF":4.4,"publicationDate":"2025-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143949031","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":"Phase field-lattice Boltzmann model for axisymmetric two-phase ferrofluid flows","authors":"Yuqi Zhu ,&nbsp;Shiting Zhang ,&nbsp;Yang Hu ,&nbsp;Xiaoqiang Yue ,&nbsp;Shi Shu ,&nbsp;Qiang He ,&nbsp;Decai Li","doi":"10.1016/j.matcom.2025.04.034","DOIUrl":"10.1016/j.matcom.2025.04.034","url":null,"abstract":"<div><div>In this paper, a phase field-based lattice Boltzmann model is developed to simulate axisymmetric two-phase ferrofluid flows. The three-population multi-relaxation time lattice Boltzmann models are constructed to solve the conservative Allen-Cahn phase field equation, the velocity-based Navier-Stokes equations, and the magnetic scalar potential equation. To deal with axisymmetric effects, some appropriate equilibrium distribution functions and discrete source/forcing terms are given. The Chapman-Enskog analysis is used to show the consistencies between the present newly proposed multi-relaxation time flow field lattice Boltzmann model and macroscopic governing equations. In the numerical validation section, the Laplace law and a sphere in a uniform magnetic field were simulated, which the simulation results show good agreement with the analytical solutions. Then several typical problems such as ferrofluid droplet deformation, Rayleigh–Plateau instability, two bubbles merging and bubble rising in ferrofluids are numerically studied to explore the mechanism of phase field interface dynamics in two-phase ferrofluid flows. As the density ratio between the two phases ranges from 1.975 to 1000, and the dynamic viscosity ratio ranges from 1 to 200, the numerical simulation results are satisfactory. This indicates that the proposed model can effectively deal with complex two-phase ferrofluid flows with large density and viscosity ratios.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"237 ","pages":"Pages 281-315"},"PeriodicalIF":4.4,"publicationDate":"2025-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143927381","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":"News of IMACS","authors":"","doi":"10.1016/S0378-4754(25)00162-4","DOIUrl":"10.1016/S0378-4754(25)00162-4","url":null,"abstract":"","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"235 ","pages":"Page 237"},"PeriodicalIF":4.4,"publicationDate":"2025-04-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143878841","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":"IMACS Calendar of Events","authors":"","doi":"10.1016/S0378-4754(25)00163-6","DOIUrl":"10.1016/S0378-4754(25)00163-6","url":null,"abstract":"","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"235 ","pages":"Page 238"},"PeriodicalIF":4.4,"publicationDate":"2025-04-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143878921","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":"Hopf bifurcation in a generalized Goodwin model with delay","authors":"Eysan Sans ,&nbsp;Melisa Akdemir ,&nbsp;Ayse Tiryakioglu ,&nbsp;Ayse Peker-Dobie ,&nbsp;Cihangir Ozemir","doi":"10.1016/j.matcom.2025.04.012","DOIUrl":"10.1016/j.matcom.2025.04.012","url":null,"abstract":"<div><div>Goodwin’s model is a cornerstone in the study of dynamical systems within macroeconomics, explaining the interaction between employment ratio and wage share in a closed economy. Analogous to predator–prey dynamics in mathematical economics, the Goodwin model, despite its simplicity, effectively captures the periodic behavior of state variables over specific time intervals. By relaxing the initial assumptions, the model can be adapted to account for more complex economic scenarios. In this article, we study a higher-dimensional extension of the Goodwin model that incorporates variable capacity utilization and capital coefficient alongside employment ratio and wage share. In particular instances, the wage share and employment rate equations decouple from the overall system. For these cases, by incorporating a delay effect in the Phillips curve, we demonstrate that while the equilibrium of the generalized system remains stable within certain parameter domains in the absence of delay, the introduction of delay can induce a Hopf bifurcation, leading to periodic oscillations. We analytically derive the critical delay parameter value that destabilizes the equilibrium point via a Hopf bifurcation.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"237 ","pages":"Pages 86-106"},"PeriodicalIF":4.4,"publicationDate":"2025-04-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143906032","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}