Mathematics and Computers in Simulation最新文献

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IF 4.4 2区数学 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Mathematics and Computers in Simulation

Pub Date : 2025-12-04 DOI: 10.1016/S0378-4754(25)00510-5

引用次数: 0

A master-slave game based shared energy storage time-of-use pricing strategy under blockchain technology 区块链技术下基于主从博弈的共享储能分时定价策略

IF 4.4 2区数学 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Mathematics and Computers in Simulation

Pub Date : 2025-12-03 DOI: 10.1016/j.matcom.2025.12.002

Wanying Li , Fugui Dong , Zhengsen Ji , Ruoyun Du

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.

针对当前储能利用效率低、收益低的问题，本文首先设计了基于智能合约的共享储能（SES）框架，明确了电网、用户聚合器、新能源聚合器和SES服务提供商之间的交易机制；其次，建立了以SES服务提供商为主导，用户聚合器为follower的主从博弈模型；提出了一种主从Stackelberg博弈时间定价方案。最后，通过算法仿真和多场景、多方法对比分析，将改进的遗传算法与Gurobi求解器相结合，对各主体的策略进行优化。结果表明，区块链技术能够有效支持SES服务提供商实现分时定价交易。采用分时定价，SES服务商的利润可达22508元，优于单一定价的4648元，同时也提升了用户聚合商和新能源聚合商的利润。存储单元的初始状态越低，利润越高。就单位大小而言，10 %-15 %的共享存储配置是最有利可图的。对于分时定价问题，改进的遗传算法优于粒子群算法和灰狼算法。

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引用次数: 0

Fractional approach to dynamic magnetic power losses in low-carbon steel under static mechanical stress and alternating magnetic field 低碳钢在静态机械应力和交变磁场作用下的动态磁功率损耗的分式方法

IF 4.4 2区数学 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Mathematics and Computers in Simulation

Pub Date : 2025-12-03 DOI: 10.1016/j.matcom.2025.12.003

Benjamin Ducharne , Abderraouf Ouazib , Mathieu Domenjoud , Patrick Fagan , Laurent Daniel

This study extends an analytical fractional approach for describing magnetic losses to thick, low-carbon steel specimens, focusing on the influence of uniaxial mechanical stress on magnetic loss variations. The main objective is to develop a simple, yet accurate analytical model for describing magnetic losses in a low-carbon steel under static mechanical stress. The model is based on a fractional-order approach that captures the material’s dissipative behavior across a wide range of frequencies and stress levels.

The high conductivity and thickness of the tested specimens amplify the classical loss contribution, making the methods using a fixed fractional derivative order

n

inadequate.

To address this, the order

n

is made dependent on the maximal value of the average flux density (

B_{a \max}

), reducing the relative Euclidean distance (RED(%)) between simulation predictions and experimental results to 5.4 % under stress-free conditions.

Under applied stress, a fitting procedure linking

n

to both maximum flux density (

B_{a \max}

) and stress

σ

achieves a RED(%) of 3.16 % across 225 data points, albeit with excessive degrees of freedom. Simplifying the definition of

n

to a three-parameter polynomial maintains reasonable accuracy (RED(%) = 6.7 %) while improving efficiency. Deviations are observed at

B_{a \max}

= 0.5 T and 1.7 T. They are attributed to specific low-field material behaviors or experimental inconsistencies.

Finally, using a sigmoid-type function with the same number of parameters achieves an improved RED(%) of 6.4 % while ensuring physical coherence.

本研究扩展了一种分析分数方法，用于描述厚的低碳钢试样的磁损失，重点关注单轴机械应力对磁损失变化的影响。主要目标是开发一种简单而准确的分析模型，用于描述静态机械应力下低碳钢的磁损失。该模型基于分数阶方法，该方法捕获了材料在广泛的频率和应力水平范围内的耗散行为。测试样品的高电导率和厚度放大了经典的损失贡献，使得使用固定分数阶导数阶数n的方法不充分。为了解决这个问题，n阶依赖于平均通量密度（Bamax）的最大值，将模拟预测和实验结果之间的相对欧几里得距离（RED(%)）在无应力条件下减少到5.4%。在施加应力下，将n与最大通量密度（Bamax）和应力σ联系起来的拟合程序在225个数据点上实现了3.16%的RED(%)，尽管自由度过高。将n的定义简化为三参数多项式，在提高效率的同时保持了合理的精度（RED(%) = 6.7%）。在Bamax = 0.5 T和1.7 T处观察到偏差。它们归因于特定的低场材料行为或实验不一致。最后，使用具有相同数量参数的s型函数，在保证物理相干性的情况下，RED（%）提高到6.4%。

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引用次数: 0

IMACS Calendar of Events IMACS事件日历

IF 4.4 2区数学 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Mathematics and Computers in Simulation

Pub Date : 2025-12-03 DOI: 10.1016/S0378-4754(25)00512-9

引用次数: 0

Higher-degree super-smooth C1 splines over a Powell–Sabin refined triangulation 基于Powell-Sabin精细三角剖分的高次超光滑C1样条

IF 4.4 2区数学 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Mathematics and Computers in Simulation

Pub Date : 2025-12-03 DOI: 10.1016/j.matcom.2025.11.035

Jan Grošelj

The paper provides a generalization of

C^{1}

quadratic splines over a Powell–Sabin refined triangulation to

C^{1}

splines of any degree greater than two. The splines are constructed by imposing maximal super-smoothness at Powell–Sabin triangle split points and reproduce polynomials to the highest possible degree. The spline spaces are characterized by functionals that induce a B-spline representation over a triangulation, i.e., a representation of splines in terms of locally supported nonnegative basis functions that form a partition of unity. This makes the considered splines readily applicable in computer aided geometric design, function approximation problems, and finite element methods for solving partial differential equations.

本文给出了在Powell-Sabin精细三角剖分上的C1二次样条的推广到任意大于2次的C1样条。样条是通过在Powell-Sabin三角形分裂点施加最大的超光滑来构造的，并将多项式复制到尽可能高的程度。样条空间的特征是在三角剖分上诱导出b样条表示的泛函，即，用局部支持的非负基函数表示的样条，这些基函数形成了一个统一的分区。这使得所考虑的样条很容易应用于计算机辅助几何设计、函数近似问题和求解偏微分方程的有限元方法。

引用次数: 0

News of IMACS IMACS新闻

IF 4.4 2区数学 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Mathematics and Computers in Simulation

Pub Date : 2025-12-03 DOI: 10.1016/S0378-4754(25)00511-7

引用次数: 0

A corrected Crank–Nicolson scheme for the time fractional parabolic integro-differential equation with nonsmooth data 具有非光滑数据的时间分数阶抛物型积分-微分方程的修正Crank-Nicolson格式

IF 4.4 2区数学 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Mathematics and Computers in Simulation

Pub Date : 2025-12-02 DOI: 10.1016/j.matcom.2025.12.001

Ao Chen , Xuejuan Chen , Yubin Yan , Wen Guo

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

O (τ^{2})

with respect to the time step size

τ

for both smooth and nonsmooth data at any fixed time

t

. 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.

本文提出了一种修正的Crank-Nicolson （CN）格式，用于求解涉及Caputo时间分数阶导数和分数阶Riemann-Liouville （R-L）积分的时间分数阶抛物型积分微分方程。采用加权移位grnwald - letnikov （WSGL）公式近似时间分数Riemann-Liouville积分。应用Crank-Nicolson格式逼近卡普托时间分数阶导数。在适当修正后，该格式在任意固定时间t对光滑和非光滑数据均获得了O（τ2）相对于时间步长τ的最优收敛阶。当与Galerkin有限元法进行空间离散时，该格式形成了一个完全离散格式。利用拉普拉斯变换技术严格建立了该方案的二阶误差估计，并通过数值算例进行了验证。

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引用次数: 0

Exploration on a class of impulsive delay integro-differential systems with fractional boundary conditions 一类具有分数边界条件的脉冲时滞积分-微分系统的探讨

IF 4.4 2区数学 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Mathematics and Computers in Simulation

Pub Date : 2025-12-02 DOI: 10.1016/j.matcom.2025.11.036

M. Latha Maheswari , R. Nandhini , Mohammad Sajid

This study investigates the existence and uniqueness of the solution for the boundary value problem (BVP) involving integro-impulsive delay differential equations with Caputo fractional derivatives. The problem incorporates nonlocal and Riemann–Liouville integral boundary conditions. Using the Banach contraction principle, we demonstrate the existence of a unique solution for this fractional BVP. Additionally, we provided numerical examples with graphical representations to illustrate and validate the theoretical results.

研究了一类具有Caputo分数阶导数的积分-脉冲时滞微分方程边值问题解的存在唯一性。该问题包含了非局部边界条件和Riemann-Liouville积分边界条件。利用Banach收缩原理，证明了该分数阶BVP的唯一解的存在性。此外，我们还提供了图形表示的数值例子来说明和验证理论结果。

引用次数: 0

Convergence analysis of a skeletal discontinuous Galerkin finite element method for time-harmonic Maxwell equations with large wave numbers 大波数时谐Maxwell方程骨架不连续Galerkin有限元法的收敛性分析

IF 4.4 2区数学 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Mathematics and Computers in Simulation

Pub Date : 2025-12-01 DOI: 10.1016/j.matcom.2025.11.039

Achyuta Ranjan Dutta Mohapatra, Bhupen Deka

This article discusses a skeletal discontinuous finite element method for approximating solutions of time-harmonic Maxwell’s equations with high wave numbers. The name justifies the method because the local degrees of freedom are associated with the skeleton of the mesh. These methods are also quite popularly known as the modified weak Galerkin methods. The proposed algorithm for the time-harmonic Maxwell equations is a parameter-free, non-conforming finite element method that uses discontinuous polynomials to approximate the true solution. Due to the choice of functions in these skeletal Galerkin methods, one has the flexibility of an inbuilt weak tangential continuity incorporated in the approximation space. Optimal order of convergence for the errors has been derived in

L^{2}

and a discretely defined

H (curl)

-norms. Numerical computations verify the theoretical convergence rates, and the proposed numerical approximation scheme is stable for the time-harmonic equations with large wave numbers.

本文讨论了一种近似高波数时谐麦克斯韦方程组解的骨架不连续有限元法。这个名字证明了这个方法的合理性，因为局部自由度与网格的骨架相关联。这些方法也被普遍称为修正弱伽辽金方法。提出的求解时谐Maxwell方程的算法是一种无参数、非一致性的有限元方法，它使用不连续多项式逼近真解。由于在这些骨架伽辽金方法中选择了函数，因此在近似空间中具有内置弱切向连续性的灵活性。在L2和离散定义的H（旋度）范数下，导出了误差的最优收敛阶。数值计算验证了理论的收敛速度，所提出的数值逼近格式对于大波数时谐方程是稳定的。

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引用次数: 0

A hybrid integer-Caputo fractional order dengue transmission model: Parameter optimization and empirical study with real-world data 一种混合整数- caputo分数阶登革热传播模型：参数优化与现实数据的实证研究

IF 4.4 2区数学 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Mathematics and Computers in Simulation

Pub Date : 2025-12-01 DOI: 10.1016/j.matcom.2025.11.040

Priyanka Harjule , Harshit , Rajesh Kumar

Dengue fever is a major viral disease that spreads through mosquitoes and is a public health concern, especially in some tropical and subtropical regions. Traditional integer-order compartmental models often do not work well at modeling how disease spreads over time, which is often affected by past infection rates and environmental factors. We propose a hybrid SEISRD-SI model that combines integer-order and fractional-order dynamics with the Caputo derivative. It also includes compartments for severe dengue and dengue-induced mortality to better represent how the disease spreads and what happens as a result. The existence and uniqueness of the fractional model are proved using the Banach Fixed Point Theorem. The basic reproduction number

R_{0}

is derived using the next generation matrix method, which provides key insights into disease spread thresholds. The hybrid model is calibrated using weekly dengue incidence data from Brazil, and parameters are optimized through Particle Swarm Optimization. The optimized hybrid model lowers the mean relative error (MRE) by up to 6.12% compared to the Caputo fractional-order model (MRE: 20.90%) and the integer-order model (MRE: 24.15%). These findings highlight the ability of hybrid modeling to capture both peak and non-peak epidemic dynamics and underscore the value of fractional calculus in advancing epidemiological modeling frameworks.

登革热是一种通过蚊子传播的主要病毒性疾病，是一个公共卫生问题，特别是在一些热带和亚热带地区。传统的整序隔间模型往往不能很好地模拟疾病如何随时间传播，这通常受到过去感染率和环境因素的影响。我们提出了一个混合SEISRD-SI模型，该模型结合了整数阶和分数阶动力学与Caputo导数。它还包括重症登革热和登革热引起的死亡率的分区，以更好地代表疾病如何传播及其后果。利用Banach不动点定理证明了分数阶模型的存在唯一性。基本繁殖数R0是使用下一代矩阵方法导出的，该方法提供了对疾病传播阈值的关键见解。混合模型使用巴西每周登革热发病率数据进行校准，并通过粒子群算法对参数进行优化。与Caputo分数阶模型（MRE为20.90%）和整数阶模型（MRE为24.15%）相比，优化后的混合模型的平均相对误差（MRE）降低了6.12%。这些发现突出了混合建模捕捉高峰和非高峰流行病动态的能力，并强调了分数微积分在推进流行病学建模框架方面的价值。

{"title":"A hybrid integer-Caputo fractional order dengue transmission model: Parameter optimization and empirical study with real-world data","authors":"Priyanka Harjule , Harshit , Rajesh Kumar","doi":"10.1016/j.matcom.2025.11.040","DOIUrl":"10.1016/j.matcom.2025.11.040","url":null,"abstract":"<div><div>Dengue fever is a major viral disease that spreads through mosquitoes and is a public health concern, especially in some tropical and subtropical regions. Traditional integer-order compartmental models often do not work well at modeling how disease spreads over time, which is often affected by past infection rates and environmental factors. We propose a hybrid SEISRD-SI model that combines integer-order and fractional-order dynamics with the Caputo derivative. It also includes compartments for severe dengue and dengue-induced mortality to better represent how the disease spreads and what happens as a result. The existence and uniqueness of the fractional model are proved using the Banach Fixed Point Theorem. The 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 method, which provides key insights into disease spread thresholds. The hybrid model is calibrated using weekly dengue incidence data from Brazil, and parameters are optimized through Particle Swarm Optimization. The optimized hybrid model lowers the mean relative error (MRE) by up to 6.12% compared to the Caputo fractional-order model (MRE: 20.90%) and the integer-order model (MRE: 24.15%). These findings highlight the ability of hybrid modeling to capture both peak and non-peak epidemic dynamics and underscore the value of fractional calculus in advancing epidemiological modeling frameworks.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"243 ","pages":"Pages 339-361"},"PeriodicalIF":4.4,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145685316","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}

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