Mathematics and Computers in Simulation最新文献

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Optimal control of chaos in a novel SITR epidemic model with generalized incidence and adaptive treatment dynamics: A deep neural network analysis 具有广义发病率和自适应治疗动力学的新型SITR流行病模型混沌的最优控制：深度神经网络分析

IF 4.4 2区数学 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Mathematics and Computers in Simulation

Pub Date : 2025-12-11 DOI: 10.1016/j.matcom.2025.12.005

A. El-Mesady , M.A. Abdelkawy , Muhammad Farhan , Mohammad Izadi

This paper introduces a novel SITR (Susceptible-Infected-Treated-Recovered) epidemic model that incorporates a Holling Type III incidence rate and a saturated treatment function to capture superspreading dynamics and finite healthcare capacity. We establish the model’s well-posedness by proving the positivity and boundedness of solutions. A comprehensive bifurcation analysis reveals that the system exhibits rich dynamical behaviors, including Transcritical, Saddle–node, and Hopf bifurcations, which delineate thresholds between disease extinction, persistence, and oscillatory states. An optimal control framework is subsequently formulated to derive effective intervention strategies. The core methodological contribution is the development of a hybrid deep neural network (DNN) architecture, utilizing Tanh and ReLU activations, to serve as a high-fidelity surrogate for the model’s complex dynamics. This approach is validated within a stochastic numerical scheme, employing a 70%–15%–15% data split for robust training and testing. The DNN achieves exceptional predictive accuracy, with a mean squared error of

1 0^{- 10}

and a minimum absolute error of

1 0^{- 8}

, demonstrating precise alignment with benchmark solutions. This work establishes a novel paradigm that integrates sophisticated dynamical systems theory with advanced deep learning, resulting in a computationally efficient and highly accurate framework for analyzing and controlling complex epidemic systems.

本文介绍了一种新的SITR（易感-感染-治疗-恢复）流行病模型，该模型结合了Holling III型发病率和饱和治疗函数，以捕捉超传播动力学和有限的医疗保健能力。通过证明解的正性和有界性，建立了模型的适定性。综合分岔分析表明，该系统表现出丰富的动力学行为，包括跨临界分岔、鞍节点分岔和Hopf分岔，它们描绘了疾病灭绝、持续和振荡状态之间的阈值。随后制定了最优控制框架，以获得有效的干预策略。核心方法贡献是开发混合深度神经网络（DNN）架构，利用Tanh和ReLU激活，作为模型复杂动态的高保真代理。该方法在随机数值方案中得到验证，采用70%-15%-15%的数据分割进行鲁棒性训练和测试。DNN实现了卓越的预测精度，均方误差为10−10，最小绝对误差为10−8，证明了与基准解决方案的精确一致性。这项工作建立了一个新的范例，将复杂的动力系统理论与先进的深度学习相结合，形成了一个计算效率高、精度高的框架，用于分析和控制复杂的流行病系统。

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Equilibrium reinsurance and investment strategies for insurers with random risk aversion under Heston’s SV model Heston的SV模型下随机风险规避保险人的均衡再保险与投资策略

IF 4.4 2区数学 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Mathematics and Computers in Simulation

Pub Date : 2025-12-08 DOI: 10.1016/j.matcom.2025.12.004

Jian-hao Kang , Zhun Gou , Nan-jing Huang

This study employs expected certainty equivalents to explore the reinsurance and investment issue pertaining to an insurer that aims to maximize the expected utility while being subject to random risk aversion. The insurer’s surplus process is modeled approximately by a drifted Brownian motion, and the financial market is comprised of a risk-free asset and a risky asset with its price depicted by Heston’s stochastic volatility (SV) model. Within a game theory framework, a strict verification theorem is formulated to delineate the equilibrium reinsurance and investment strategies as well as the corresponding value function. Furthermore, through solving the pseudo Hamilton–Jacobi–Bellman (HJB) system, semi-analytical formulations for the equilibrium reinsurance and investment strategies and the associated value function are obtained under the exponential utility. Additionally, several numerical experiments are carried out to demonstrate the characteristics of the equilibrium reinsurance and investment strategies.

本研究运用预期确定性等价物，探讨以预期效用最大化为目标的保险公司在随机风险规避下的再保险与投资问题。保险公司的盈余过程用漂移布朗运动近似建模，金融市场由无风险资产和风险资产组成，其价格由赫斯顿随机波动率（SV）模型描述。在博弈论的框架下，提出了一个严格的验证定理来描述均衡再保险和投资策略以及相应的价值函数。进一步，通过求解伪Hamilton-Jacobi-Bellman （HJB）系统，得到了指数效用下均衡再保险和投资策略及其相关价值函数的半解析表达式。此外，通过数值实验验证了均衡再保险和均衡投资策略的特点。

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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)00509-9

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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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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。

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IF 4.4 2区数学 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Mathematics and Computers in Simulation

Pub Date : 2025-12-03 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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