Mathematics and Computers in Simulation最新文献

{"title":"An RBF-based method with optimal point selection for solving two-dimensional multi-term time-fractional PIDEs with weakly singular kernels","authors":"M. Fardi,&nbsp;B. Raeisi,&nbsp;M. Ahmadi Darani","doi":"10.1016/j.matcom.2025.11.013","DOIUrl":"10.1016/j.matcom.2025.11.013","url":null,"abstract":"<div><div>This paper presents a novel numerical method using radial basis functions (RBFs) to solve two-dimensional multi-term time-fractional partial integro-differential equations with multi-term weakly singular kernels. The spatial discretization is based on an RBF-generated finite difference method, combined with geometrically optimal point selection for efficient stencil design. The key contribution of this study is the development of a greedy algorithm that constructs quasi-uniform point sets by balancing the fill distance and separation distance, thereby ensuring asymptotically optimal domain coverage. By generating weights with desirable properties, the method significantly enhances stability. A series of numerical experiments has been conducted to evaluate the efficiency and accuracy of the proposed method. The results, presented through detailed tables and figures, confirm the method’s effectiveness in accurately solving the target equations. Furthermore, performance evaluations using various examples highlight the method’s superiority and reliability.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"242 ","pages":"Pages 96-120"},"PeriodicalIF":4.4,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145580119","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":"Analysis and computation of turning points in optical straight and bent waveguides","authors":"Rakesh Kumar Dhiman","doi":"10.1016/j.matcom.2025.11.004","DOIUrl":"10.1016/j.matcom.2025.11.004","url":null,"abstract":"<div><div>In this work, we investigate the turning points where the model’s behavior diverges significantly from other points within the domain. These points play a crucial role in shaping the overall dynamics and characteristics of the system. We provide a comprehensive study of turning points in optical waveguides with three-layer constant step-index profiles, addressing both their mathematical and physical aspects.</div><div>A general mathematical formula is introduced to determine the exact locations of all possible turning points for different TE and TM modes in one-dimensional straight and bent waveguides. The number and positions of these turning points depend on parameters such as the bent radius, refractive index profiles, and mode properties, which are analyzed in detail.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"242 ","pages":"Pages 84-95"},"PeriodicalIF":4.4,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145580120","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":"Gradient like optimization technique with finite element method to quantify the uncertainties under interval type 2 fuzzy environments","authors":"Paresh Kumar Panigrahi ,&nbsp;Sukanta Nayak ,&nbsp;Oscar Castillo","doi":"10.1016/j.matcom.2025.07.049","DOIUrl":"10.1016/j.matcom.2025.07.049","url":null,"abstract":"<div><div>This study proposes a technique to quantify uncertainties in structural engineering systems under interval type 2 fuzzy (IT2F) environments. The finite element method (FEM) is combined with optimization approach to investigate the field variables with interval type 2 fuzzy uncertainties. To address these exclusive features, here the interval type 2 fuzzy finite element method can be incorporated to discretized the element and transformed the governing differential equation into algebraic equations. To estimate the field variables that are getting affected by uncertain parameters, the authors have proposed IT2F gradient descent optimization (IT2FGDO) algorithm. The uncertainties are taken in interval type 2 fuzzy environment. To validate the proposed algorithm, convergence analysis is performed. The result show significant differences and uncertain analysis of structure with different temperature. Then, two cases were considered to quantify the uncertainty and established the stability condition of the systems. It is guaranteed that the solution of IT2FGDO technique possess less uncertainty in interval type 2 fuzzy environment.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"242 ","pages":"Pages 164-198"},"PeriodicalIF":4.4,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145580122","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":"Memory tracing in fractional-order modeling of HIV/AIDS: Analyzing periodic transmission, anxiety, economic constraints, and treatment barriers","authors":"Silajit Kar ,&nbsp;Dilip Kumar Maiti ,&nbsp;Atasi Patra Maiti","doi":"10.1016/j.matcom.2025.11.017","DOIUrl":"10.1016/j.matcom.2025.11.017","url":null,"abstract":"<div><h3>Model Framework:</h3><div>This study introduces a new HIV/AIDS model utilizing the Caputo fractional-order derivative to capture disease dynamics under realistic conditions. The model incorporates media-driven awareness and local communication to inform susceptible populations, while accounting for how psychological anxiety impacts infection rates among aware individuals. We incorporated both fixed and periodic disease transmission rates into our model. It also includes a diagnostic process for identifying CD4+ T cell count in asymptomatic cases, alongside treatment functions that consider medical resource limitations to enhance real-world applicability. An individual’s economic status for accessing treatment is also taken into account. Both sides of the model equations are dimensionally balanced.</div></div><div><h3>Analytical-Numerical Experiments:</h3><div>Analytical results show a unique positive solution with both HIV/AIDS-free and infected equilibria. The fractional-order dependent basic reproduction number <span><math><msub><mrow><mi>R</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span> is derived using the next-generation matrix, and the Routh–Hurwitz criterion confirms the local stability of the infected equilibrium. Numerical simulations with the Adams–Bashforth-Moulton method validate these findings, demonstrating how variations in <span><math><mi>α</mi></math></span>, diagnosis rate, awareness delay, psychological anxiety, individual’s economic status, resource availability, and periodic disease transmission rate affect system dynamics.</div></div><div><h3>Fractional Order, Memory Tracing, and Periodic Transmission on Disease Dynamics:</h3><div>The study analyzes how the fractional order <span><math><mi>α</mi></math></span> and memory kernel influence system dynamics and disease transmission control during transitional phases. Spectral analysis reveals periodic instabilities from oscillations in transmission rates, showing that increased transmission can stabilize the system but also raises secondary infections and <span><math><msub><mrow><mi>R</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span>. The study examines the effects of <span><math><mi>α</mi></math></span> and oscillation period on system behavior. Using the <span><math><mrow><mi>L</mi><mn>1</mn></mrow></math></span> scheme, memory evolution is visualized, showing that memory trace decreases as <span><math><mi>α</mi></math></span> increases from 0 to 1 and diminishes at 1, highlighting distinctions between integer and non-integer order derivatives. These insights aid in understanding outbreaks and improving future forecasts and mitigation strategies.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"242 ","pages":"Pages 199-229"},"PeriodicalIF":4.4,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145624689","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 master-slave game based shared energy storage time-of-use pricing strategy under blockchain technology","authors":"Wanying Li ,&nbsp;Fugui Dong ,&nbsp;Zhengsen Ji ,&nbsp;Ruoyun Du","doi":"10.1016/j.matcom.2025.12.002","DOIUrl":"10.1016/j.matcom.2025.12.002","url":null,"abstract":"<div><div>To address the current problems of low energy storage utilization efficiency and income, this study first designs a smart contract-based shared energy storage (SES) framework, which specifies the transaction mechanisms among the grid, user aggregator, new energy aggregator, and SES service provider. Second, a master-slave game model is established with the SES service provider as the leader and the user aggregator, and new energy aggregator as the followers. A master-multi-slave Stackelberg game time-of-use pricing solution is proposed. Finally, arithmetic simulation and multi-scenario, multi-method comparative analysis are performed to optimize the strategies of each subject using the improved genetic algorithm combined with the Gurobi solver. The results show that blockchain technology can effectively support SES service providers to realize time-of-use pricing transactions. With time-of-use pricing, the profit of the SES service provider can reach 22508 yuan, which is better than single pricing of 4648 yuan, and also improves the profits of the user aggregator and new energy aggregator. More profit is made when the initial state of the storage unit is low. 10 %-15 % of shared storage configurations are the most profitable in terms of unit size. For time-of-use pricing problem, the improved genetic algorithm outperforms particle swarm and gray wolf algorithms.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"242 ","pages":"Pages 323-342"},"PeriodicalIF":4.4,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145747267","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":"Improved stability analysis for quaternion-valued neural networks with proportional and mixed time-varying delays","authors":"Yang Cao ,&nbsp;Jincy Jacob ,&nbsp;S. Dharani ,&nbsp;M. Sivakumar","doi":"10.1016/j.matcom.2025.11.005","DOIUrl":"10.1016/j.matcom.2025.11.005","url":null,"abstract":"<div><div>The stability of mixed time-varying delayed and proportional delayed Quaternion-Valued Neural Networks (QVNNs) is investigated herein. We contemplate the QVNNs as a single entity, as opposed to dissecting them into separate Complex-Valued Neural Networks (CVNNs) or Real-Valued Neural Networks(RVNNs). By employing Lyapunov–Krasovskii Functionals (LKF) with free weight matrices and linear matrix inequalities (LMI), sufficient conditions for global asymptotic stability are obtained for the proposed model. To show the usefulness of the derived theoretical deductions, a numerical illustration is offered at the end.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"242 ","pages":"Pages 270-278"},"PeriodicalIF":4.4,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145693937","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":"Efficient energy-stable numerical methods for phase-field vesicle membrane models with strict volume and surface area constraints","authors":"Jingjing Song ,&nbsp;Yanqing He ,&nbsp;Qi Li","doi":"10.1016/j.matcom.2025.11.011","DOIUrl":"10.1016/j.matcom.2025.11.011","url":null,"abstract":"<div><div>We propose a new phase-field vesicle model that rigorously enforces physical constraints and admits efficient, energy-stable numerical discretizations. The model couples a conserved Allen–Cahn gradient flow, which guarantees exact preservation of the enclosed volume, with a single Lagrange multiplier that imposes the global surface area constraint. Based on this formulation, we design two classes of numerical schemes. The first is a linear SAV-based framework that is simple to implement and reduces each time step to constant-coefficient linear solves. The second is a new Lagrange multiplier scheme that retains the efficiency of SAV while exactly preserving the physical constraints and strictly dissipating the original free energy, requiring only two inexpensive nonlinear solves per step. For both schemes, we establish discrete energy dissipation laws, provide implementation details, and validate their performance through extensive 2D and 3D simulations. Numerical results confirm accuracy, unconditional stability, exact constraint preservation, and computational efficiency, demonstrating the effectiveness of the proposed approaches for simulating vesicle dynamics.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"242 ","pages":"Pages 36-53"},"PeriodicalIF":4.4,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145532419","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 corrected Crank–Nicolson scheme for the time fractional parabolic integro-differential equation with nonsmooth data","authors":"Ao Chen ,&nbsp;Xuejuan Chen ,&nbsp;Yubin Yan ,&nbsp;Wen Guo","doi":"10.1016/j.matcom.2025.12.001","DOIUrl":"10.1016/j.matcom.2025.12.001","url":null,"abstract":"<div><div>This paper proposes a corrected Crank–Nicolson (CN) scheme for solving time fractional parabolic integro-differential equations which involve Caputo time fractional derivative and fractional Riemann–Liouville (R-L) integral. The weighted and shifted Grünwald–Letnikov (WSGL) formulae is adopted to approximate the time fractional Riemann–Liouville integral. The Crank–Nicolson scheme is applied to approximate the Caputo time fractional derivative. After appropriating corrections, the proposed scheme attains the optimal convergence order of <span><math><mrow><mi>O</mi><mrow><mo>(</mo><msup><mrow><mi>τ</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo></mrow></mrow></math></span> with respect to the time step size <span><math><mi>τ</mi></math></span> for both smooth and nonsmooth data at any fixed time <span><math><mi>t</mi></math></span>. When combined with the Galerkin finite element method for spatial discretization, it forms a fully discrete scheme. The second-order error estimate for this scheme is rigorously established using the Laplace transform technique and verified by some numerical examples.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"242 ","pages":"Pages 279-296"},"PeriodicalIF":4.4,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145693939","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":"Sizing methodology and optimal location of superconducting fault current limiter in DC substations for railways applications","authors":"Willy Magloire Nkounga ,&nbsp;Khaled Almaksour ,&nbsp;Arnaud Allais ,&nbsp;Hervé Caron ,&nbsp;Christophe Saudemont ,&nbsp;Benoit Robyns","doi":"10.1016/j.matcom.2025.11.010","DOIUrl":"10.1016/j.matcom.2025.11.010","url":null,"abstract":"<div><div>The main innovation of this work is proposing a lifespan economic assessment for resistive superconducting faults current limiter (rSFCL) and a sizing methodology for the rSFCL impedance in railways DC substations. In the presence of short-circuit fault, the current can reach up to 30 times its nominal value. A sizing methodology for rSFCL is developed and applied in the presence of faults. Optimization of REBCO tapes is proposed through heat exchange using MATLAB and EMTP-RV, followed by application for fault limitation. Finally, an investigation of several rSFCL positions is conducted to determine the optimal location for better sizing of the circuit breakers. A cost assessment of the system is conducted. A case study is conducted using three <span><math><mrow><mn>1500</mn><mspace></mspace><mtext>V-</mtext><mn>4</mn><mspace></mspace><mtext>kA</mtext></mrow></math></span> DC substations with a fault current value of 120 kA. The results show that the rSFCL can limit up to 66.7% the fault current and reduce the size of the circuit breaker by 50%. The substation with the rSFCL offers a minimum total expenditure (TOTEX), comprising CAPEX (capital expenditure) and OPEX (operational expenditure), profitability of 15.5% compared to a traditional substation.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"242 ","pages":"Pages 1-18"},"PeriodicalIF":4.4,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145532421","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":"The impact of human shields in autonomous and non-autonomous prey–predator models with modified Cosner functional response","authors":"Subarna Roy ,&nbsp;Dina Sultan AL-Jaf ,&nbsp;Ashraf Adnan Thirthar ,&nbsp;Pankaj Kumar Tiwari","doi":"10.1016/j.matcom.2025.11.016","DOIUrl":"10.1016/j.matcom.2025.11.016","url":null,"abstract":"<div><div>In this study, we investigate the complex interplay between prey and predators under varying human-mediated influences. Theoretical analyses explore the solution’s non-negativity and boundedness, existence of feasible equilibria and their stability behaviors, and various bifurcations including saddle–node and Hopf. Using a detailed numerical exploration, we identified distinct population distribution, demonstrating how different factors shape ecological systems in non-trivial ways. The results suggest that human interventions, whether through direct shielding of prey or indirect effects on predator–prey interactions, can significantly disrupt ecological dynamics. Our findings highlight the importance of sustainable strategies that conserve prey populations while supporting predators to maintain ecosystem balance. Furthermore, by adding seasonal changes to some key parameters, we extend our autonomous system to a nonautonomous framework. Simple periodic oscillations, higher periodic oscillations, bursting patterns, and the extinction of predators are observed due to seasonal changes in the parameters.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"242 ","pages":"Pages 54-73"},"PeriodicalIF":4.4,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145532418","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}