Mathematics and Computers in Simulation最新文献

英文中文

Shifted Chebyshev collocation with CESTAC-CADNA-based instability detection for nonlinear Volterra–Hammerstein integral equations 基于cestac - cadna的非线性Volterra-Hammerstein积分方程不稳定性检测的移位Chebyshev搭配

IF 4.4 2区数学 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Mathematics and Computers in Simulation

Pub Date : 2026-08-01 Epub Date: 2026-01-28 DOI: 10.1016/j.matcom.2026.01.029

Walid Remili , Samad Noeiaghdam

This paper introduces a high-order numerical method for the solution of nonlinear Volterra–Hammerstein integral equations (NVHIEs) with smooth and weakly singular kernels, based on the collocation approach. The proposed method employs a collocation scheme with shifted Chebyshev polynomials (SCPs), combined with an appropriate variable transformation, to reduce the integral equation to a nonlinear algebraic system. We rigorously analyze the convergence properties of the collocation method, establishing its theoretical validity and proving a specific convergence rate of

O (N^{3 / 4 - m})

, which highlights the rigor and efficiency of the approach. To ensure reliable error control and stability, we integrate the CESTAC (Contrôle et Estimation Stochastique des Arrondis de Calculs) method and the CADNA (Control of Accuracy and Debugging for Numerical Applications) library, providing a unified framework that identifies numerical instabilities (self-validation, mathematical, branching, and intrinsic) while also determining the optimal step size, optimal approximation, and optimal error. Several numerical examples are presented and compared with existing methods to illustrate the enhanced efficiency and accuracy of our approach.

本文介绍了一种基于配点法求解光滑弱奇异核非线性Volterra-Hammerstein积分方程的高阶数值方法。该方法采用平移切比雪夫多项式（SCPs）搭配方案，结合适当的变量变换，将积分方程简化为非线性代数系统。我们严格分析了该方法的收敛性，建立了该方法的理论有效性，并证明了其特定的收敛速度为0 (N3/4−m)，从而突出了该方法的严谨性和有效性。为了确保可靠的误差控制和稳定性，我们集成了CESTAC （Contrôle et Estimation Stochastique des Arrondis de Calculs）方法和CADNA（精度控制和数值应用调试）库，提供了一个统一的框架，可以识别数值不稳定性（自我验证、数学、分支和内在），同时确定最佳步长、最佳近似和最佳误差。给出了几个数值算例，并与现有方法进行了比较，以说明本文方法提高了效率和精度。

{"title":"Shifted Chebyshev collocation with CESTAC-CADNA-based instability detection for nonlinear Volterra–Hammerstein integral equations","authors":"Walid Remili , Samad Noeiaghdam","doi":"10.1016/j.matcom.2026.01.029","DOIUrl":"10.1016/j.matcom.2026.01.029","url":null,"abstract":"<div><div>This paper introduces a high-order numerical method for the solution of nonlinear Volterra–Hammerstein integral equations (NVHIEs) with smooth and weakly singular kernels, based on the collocation approach. The proposed method employs a collocation scheme with shifted Chebyshev polynomials (SCPs), combined with an appropriate variable transformation, to reduce the integral equation to a nonlinear algebraic system. We rigorously analyze the convergence properties of the collocation method, establishing its theoretical validity and proving a specific convergence rate of <span><math><mrow><mi>O</mi><mrow><mo>(</mo><msup><mrow><mi>N</mi></mrow><mrow><mn>3</mn><mo>/</mo><mn>4</mn><mo>−</mo><mi>m</mi></mrow></msup><mo>)</mo></mrow></mrow></math></span>, which highlights the rigor and efficiency of the approach. To ensure reliable error control and stability, we integrate the CESTAC (Contrôle et Estimation Stochastique des Arrondis de Calculs) method and the CADNA (Control of Accuracy and Debugging for Numerical Applications) library, providing a unified framework that identifies numerical instabilities (self-validation, mathematical, branching, and intrinsic) while also determining the optimal step size, optimal approximation, and optimal error. Several numerical examples are presented and compared with existing methods to illustrate the enhanced efficiency and accuracy of our approach.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"246 ","pages":"Pages 60-77"},"PeriodicalIF":4.4,"publicationDate":"2026-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146081412","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}

引用次数: 0

Approximation of generalized time fractional derivatives: Error analysis via scale and weight functions 广义时间分数阶导数的近似：通过尺度和权重函数的误差分析

IF 4.4 2区数学 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Mathematics and Computers in Simulation

Pub Date : 2026-08-01 Epub Date: 2026-01-24 DOI: 10.1016/j.matcom.2026.01.027

Vikash Sharma, Vineet Kumar Singh

In this manuscript, we investigate various properties of the Generalized time fractional derivative (GTFD). We establish several regularity results and derive bounds in specific spaces like

C^{1}, W^{1, 1}

that characterize the behavior of the GTFD operator. Furthermore, we propose an efficient hybrid computational approximation to approximate the GTFD of order

α \in (0, 1)

, applicable to smooth and non-smooth solutions. This approximation is based on a Newton interpolation polynomial of arbitrary finite degree. The role of scale and weight functions in influencing the local truncation error and convergence order is thoroughly analyzed, with numerical experiments providing validation of these theoretical insights. The proposed approximation is further utilized to construct a computational scheme for solving the general time fractional diffusion equation (GTFDE), for which we rigorously establish uniqueness and convergence, while stability is proven specifically for linear interpolation. Numerical examples are utilized to verify that our scheme is more efficient compared to the existing schemes (Stynes et al., 2017, Z. wang, 2025 and Xu et al., 2013). Without loss of generality, numerical results are presented for linear and quadratic interpolation, confirming the approximation’s accuracy and consistency with theoretical predictions.

本文研究了广义时间分数阶导数（GTFD）的各种性质。我们建立了几个正则性结果，并在C1，W1,1等特定空间中推导了表征GTFD算子行为的界。此外，我们提出了一种有效的混合计算近似来近似阶α∈(0,1)的GTFD，适用于光滑和非光滑解。这种近似是基于任意有限次的牛顿插值多项式。深入分析了尺度函数和权函数对局部截断误差和收敛阶的影响，并通过数值实验验证了这些理论见解。进一步利用所提出的近似构造了求解一般时间分数扩散方程（GTFDE）的计算格式，并严格建立了该格式的唯一性和收敛性，同时证明了该格式在线性插值下的稳定性。数值算例验证了我们的方案比现有方案更高效（Stynes et al., 2017， Z. wang, 2025 and Xu et al., 2013）。在不丧失一般性的情况下，给出了线性和二次插值的数值结果，证实了近似的准确性和与理论预测的一致性。

{"title":"Approximation of generalized time fractional derivatives: Error analysis via scale and weight functions","authors":"Vikash Sharma, Vineet Kumar Singh","doi":"10.1016/j.matcom.2026.01.027","DOIUrl":"10.1016/j.matcom.2026.01.027","url":null,"abstract":"<div><div>In this manuscript, we investigate various properties of the Generalized time fractional derivative (GTFD). We establish several regularity results and derive bounds in specific spaces like <span><math><mrow><msup><mrow><mi>C</mi></mrow><mrow><mn>1</mn></mrow></msup><mo>,</mo><msup><mrow><mi>W</mi></mrow><mrow><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msup></mrow></math></span> that characterize the behavior of the GTFD operator. Furthermore, we propose an efficient hybrid computational approximation to approximate the GTFD of order <span><math><mrow><mi>α</mi><mo>∈</mo><mrow><mo>(</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>)</mo></mrow></mrow></math></span>, applicable to smooth and non-smooth solutions. This approximation is based on a Newton interpolation polynomial of arbitrary finite degree. The role of scale and weight functions in influencing the local truncation error and convergence order is thoroughly analyzed, with numerical experiments providing validation of these theoretical insights. The proposed approximation is further utilized to construct a computational scheme for solving the general time fractional diffusion equation (GTFDE), for which we rigorously establish uniqueness and convergence, while stability is proven specifically for linear interpolation. Numerical examples are utilized to verify that our scheme is more efficient compared to the existing schemes (Stynes et al., 2017, Z. wang, 2025 and Xu et al., 2013). Without loss of generality, numerical results are presented for linear and quadratic interpolation, confirming the approximation’s accuracy and consistency with theoretical predictions.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"246 ","pages":"Pages 1-24"},"PeriodicalIF":4.4,"publicationDate":"2026-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146057483","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}

引用次数: 0

Dynamics analysis of a Filippov Lymantria dispar-Great tit model with double Allee effects and two-thresholds control 具有双Allee效应和双阈值控制的Filippov Lymantria差异-大山雀模型的动力学分析

IF 4.4 2区数学 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Mathematics and Computers in Simulation

Pub Date : 2026-08-01 Epub Date: 2026-01-23 DOI: 10.1016/j.matcom.2026.01.028

Xiaoquan Kong , Ruizhi Yang

This study focuses on the Lymantria dispar-Great tit ecosystem, constructing a Filippov model with double Allee effects and proposing an integrated control strategy based on two thresholds for both pest density and natural enemy abundance. Through stability analysis of equilibria and sliding mode dynamics, the study reveals the existence of multiple sliding segments and pseudo-equilibria in the system, which can induce rich sliding bifurcation behaviors. Further investigation uncovers complex dynamical patterns under different threshold conditions, including sliding bifurcations as well as local and global bifurcations. Partial Rank Correlation Coefficient based global sensitivity analysis identifies key parameters influencing the system dynamics. The research demonstrates that appropriate setting of these two thresholds is crucial for achieving sustainable control of Lymantria dispar, while the synergistic effect of biological control and natural enemy release is essential for maintaining ecological balance.

本文以Lymantria - great tit生态系统为研究对象，构建了具有双Allee效应的Filippov模型，提出了基于害虫密度和天敌丰度两个阈值的综合防治策略。通过平衡态和滑模动力学稳定性分析，揭示了系统中存在多个滑动段和伪平衡态，从而引发丰富的滑动分岔行为。进一步的研究揭示了不同阈值条件下复杂的动力学模式，包括滑动分岔以及局部和全局分岔。基于偏秩相关系数的全局敏感性分析识别出影响系统动力学的关键参数。研究表明，合理设置这两个阈值对于实现野毒的可持续控制至关重要，而生物防治与天敌释放的协同效应对于维持生态平衡至关重要。

引用次数: 0

Robust non-singular fixed-time sliding mode control for robot manipulators: Franka robot arm 机器人机械臂的鲁棒非奇异定时滑模控制：Franka机械臂

IF 4.4 2区数学 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Mathematics and Computers in Simulation

Pub Date : 2026-08-01 Epub Date: 2026-01-16 DOI: 10.1016/j.matcom.2026.01.010

Amine Mebarki, Moussa Labbadi, Mohamed Zerrougui

Modern robotic applications demand precise trajectory tracking, which is particularly challenging due to the nonlinear dynamics, model uncertainties, and external disturbances inherent in robotic manipulators. Robust control strategies, such as Sliding Mode Control (SMC), have proven effective in addressing these challenges. Advanced variants, including finite-time and fixed-time SMC, offer the added advantage of ensuring stabilization within a predefined time frame. This paper proposes various strategies for the Franka robot, ensuring global fixed-time convergence of the closed-loop system with a singularity-free design and the settling time estimation is independent of initial conditions. A non-singular terminal sliding surface is utilized to achieve precise trajectory tracking, enhanced robustness to external disturbances, and simplified implementation. The effectiveness of the proposed methods is validated through realistic simulations of the Franka robot.

现代机器人应用需要精确的轨迹跟踪，由于非线性动力学、模型不确定性和机器人操纵器固有的外部干扰，这尤其具有挑战性。事实证明，滑模控制（SMC）等鲁棒控制策略在解决这些挑战方面是有效的。高级版本，包括有限时间和固定时间SMC，提供了额外的优势，确保在预定义的时间范围内稳定。本文针对Franka机器人提出了各种策略，保证了闭环系统的全局定时收敛，具有无奇点设计，且沉降时间估计与初始条件无关。利用非奇异终端滑动面实现精确的轨迹跟踪，增强了对外界干扰的鲁棒性，简化了实现。通过对Franka机器人的仿真，验证了所提方法的有效性。

引用次数: 0

Secure synchronization of T–S fuzzy complex dynamical networks under critical-data-targeted DoS attacks 关键数据DoS攻击下T-S模糊复杂动态网络的安全同步

IF 4.4 2区数学 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Mathematics and Computers in Simulation

Pub Date : 2026-07-01 Epub Date: 2026-01-10 DOI: 10.1016/j.matcom.2026.01.007

Jinyuan Zhang , Yuechao Ma

This article focuses on the pinning synchronization issue for Takagi–Sugeno (T–S) fuzzy complex dynamical networks (CDNs) under critical-data-targeted denial-of-service (DoS) attacks. Firstly, a novel critical-data-targeted DoS attack method is considered for the attacker to enhance the destructiveness of the attack against various nodes. Contrasting with most existing DoS attack models, this attack scheme can selectively attack critical data, allowing the attacker to cause relatively large damage to system performance. Secondly, we establish a new pinning synchronization control model for T–S fuzzy CDNs with random coupling delays. It can describe the actual world more accurately compared with the general model of CDNs. And the issue of asynchronous premise variables is solved. Furthermore, a new secure synchronization criterion is presented by leveraging the appropriate Lyapunov–Krasovskii function to realize the

H_{\infty}

performance of the system against critical-data-targeted DoS attacks. Finally, three examples are offered to confirm the efficacy of the suggested results.

本文主要研究了针对关键数据的拒绝服务（DoS）攻击下的Takagi-Sugeno （T-S）模糊复杂动态网络（cdn）的钉住同步问题。首先，提出了一种新的针对关键数据的DoS攻击方法，增强了攻击对各节点的破坏性。与大多数现有的DoS攻击模型相比，该攻击方案可以选择性地攻击关键数据，使攻击者能够对系统性能造成较大的损害。其次，针对具有随机耦合延迟的T-S模糊cdn，建立了新的钉住同步控制模型。与cdn的一般模型相比，它能更准确地描述现实世界。解决了异步前提变量的问题。此外，利用适当的Lyapunov-Krasovskii函数提出了一种新的安全同步准则，以实现系统对针对关键数据的DoS攻击的H∞性能。最后，通过三个算例验证了建议结果的有效性。

{"title":"Secure synchronization of T–S fuzzy complex dynamical networks under critical-data-targeted DoS attacks","authors":"Jinyuan Zhang , Yuechao Ma","doi":"10.1016/j.matcom.2026.01.007","DOIUrl":"10.1016/j.matcom.2026.01.007","url":null,"abstract":"<div><div>This article focuses on the pinning synchronization issue for Takagi–Sugeno (T–S) fuzzy complex dynamical networks (CDNs) under critical-data-targeted denial-of-service (DoS) attacks. Firstly, a novel critical-data-targeted DoS attack method is considered for the attacker to enhance the destructiveness of the attack against various nodes. Contrasting with most existing DoS attack models, this attack scheme can selectively attack critical data, allowing the attacker to cause relatively large damage to system performance. Secondly, we establish a new pinning synchronization control model for T–S fuzzy CDNs with random coupling delays. It can describe the actual world more accurately compared with the general model of CDNs. And the issue of asynchronous premise variables is solved. Furthermore, a new secure synchronization criterion is presented by leveraging the appropriate Lyapunov–Krasovskii function to realize the <span><math><msub><mrow><mi>H</mi></mrow><mrow><mi>∞</mi></mrow></msub></math></span> performance of the system against critical-data-targeted DoS attacks. Finally, three examples are offered to confirm the efficacy of the suggested results.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"245 ","pages":"Pages 95-113"},"PeriodicalIF":4.4,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145980217","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}

引用次数: 0

An insight on some properties of high order nonstandard linear multistep methods 关于高阶非标准线性多步方法若干性质的认识

IF 4.4 2区数学 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Mathematics and Computers in Simulation

Pub Date : 2026-07-01 Epub Date: 2026-01-17 DOI: 10.1016/j.matcom.2026.01.015

B. Takacs

In this paper, nonstandard multistep methods are considered. It is shown that under some (sufficient and necessary) conditions, these methods attain the same order as their standard counterpart — to prove this statement, a nonstandard version of Taylor’s series is constructed. The preservation of some qualitative properties (boundedness, the linear combination of the components, and a property similar to monotonicity) is also proven for all step sizes. The methods are applied to a one-dimensional equation and a system of equations, in which the numerical experiments confirm the theoretical results.

本文考虑了非标准多步法。证明了在某些（充分必要）条件下，这些方法与它们的标准对应物获得相同的阶数——为了证明这一说法，构造了一个非标准版本的泰勒级数。对于所有步长，还证明了一些定性性质（有界性，分量的线性组合以及类似于单调性的性质）的保留。将该方法应用于一维方程和方程组，并通过数值实验验证了理论结果。

引用次数: 0

Modified Armijo line search in optimization on Riemannian submanifolds with reduced computational cost 改进的Armijo线搜索在黎曼子流形优化中的应用，减少了计算量

IF 4.4 2区数学 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Mathematics and Computers in Simulation

Pub Date : 2026-07-01 Epub Date: 2026-01-06 DOI: 10.1016/j.matcom.2026.01.003

Hiroyuki Sato , Yuya Yamakawa , Kensuke Aihara

For optimization problems on Riemannian manifolds, many types of globally convergent algorithms have been proposed, and they are often equipped with the Riemannian version of the Armijo line search for global convergence. Such existing methods need to compute the value of a retraction mapping regarding the search direction several times at each iteration; this may result in high computational costs, particularly if computing the value of the retraction is expensive. To address this issue, this study focuses on embedded Riemannian submanifolds of the Euclidean spaces and proposes a novel Riemannian line search that achieves lower computational cost by incorporating a new strategy that computes the retraction only when inevitable. A class of Riemannian optimization algorithms, including the steepest descent and Newton methods, with the new line search strategy is proposed and proved to be globally convergent. Furthermore, numerical experiments on solving optimization problems on several types of embedded Riemannian submanifolds illustrate that the proposed methods are superior to the standard Riemannian Armijo line search-based methods.

对于黎曼流形上的优化问题，已经提出了许多类型的全局收敛算法，它们通常配备黎曼版本的Armijo线搜索来实现全局收敛。现有方法需要在每次迭代中多次计算关于搜索方向的缩回映射的值；这可能导致较高的计算成本，特别是如果计算收回的价值是昂贵的。为了解决这一问题，本研究将重点放在欧几里得空间的嵌入式黎曼子流形上，并提出了一种新的黎曼线搜索方法，该方法通过结合一种新的策略来降低计算成本，该策略只在不可避免的情况下计算缩回。提出了一类包含最陡下降法和牛顿法的黎曼优化算法，并证明了该算法具有全局收敛性。此外，对几种嵌入式黎曼子流形的优化问题进行了数值实验，结果表明该方法优于标准黎曼Armijo线搜索方法。

{"title":"Modified Armijo line search in optimization on Riemannian submanifolds with reduced computational cost","authors":"Hiroyuki Sato , Yuya Yamakawa , Kensuke Aihara","doi":"10.1016/j.matcom.2026.01.003","DOIUrl":"10.1016/j.matcom.2026.01.003","url":null,"abstract":"<div><div>For optimization problems on Riemannian manifolds, many types of globally convergent algorithms have been proposed, and they are often equipped with the Riemannian version of the Armijo line search for global convergence. Such existing methods need to compute the value of a retraction mapping regarding the search direction several times at each iteration; this may result in high computational costs, particularly if computing the value of the retraction is expensive. To address this issue, this study focuses on embedded Riemannian submanifolds of the Euclidean spaces and proposes a novel Riemannian line search that achieves lower computational cost by incorporating a new strategy that computes the retraction only when inevitable. A class of Riemannian optimization algorithms, including the steepest descent and Newton methods, with the new line search strategy is proposed and proved to be globally convergent. Furthermore, numerical experiments on solving optimization problems on several types of embedded Riemannian submanifolds illustrate that the proposed methods are superior to the standard Riemannian Armijo line search-based methods.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"245 ","pages":"Pages 260-274"},"PeriodicalIF":4.4,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146038828","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}

引用次数: 0

S-ERKN methods solving Maxwell’s equations in source field under wide range of boundary conditions S-ERKN方法在宽边界条件下求解源场麦克斯韦方程组

IF 4.4 2区数学 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Mathematics and Computers in Simulation

Pub Date : 2026-07-01 Epub Date: 2026-01-16 DOI: 10.1016/j.matcom.2026.01.017

Hongli Yang , Xianyang Zeng , Hao Yu

For Maxwell’s equations for isotropic homogeneous media in a cubic domain, there have been few methods that can solve almost all problems under various boundary conditions in source field since the boundary conditions and the sources are diverse, by now. Fortunately, in this paper, we succeeded in giving a unified class of methods (called S-ERKN methods) that solve problems under a wide range of boundary conditions in source field. At first, we gave a detailed study on the spatial discretization to have a so-called semi-discrete system. Here we concluded that the boundary conditions had an unsurprising impact on the differentiation matrix (denoted as

L_{U}

in this paper) but had an unexpected effect on the perturbation term (denoted as

{\tilde{F}}_{U}

in this paper) of the semi-discrete system. Secondly, we chose the ERKN (Extended Runge–Kutta Nystrom) methods as the temporal solver to improve the temporal order which is normally limited to 2 in many traditional numerical solutions. To make the S-ERKN method (obtained by the spatial and temporal discretization shown above) easy to code at low cost, we studied the fast calculation of the matrix vector product

L_{U} V

, which is the basic computational unit of the method. In this paper, we also performed the divergence analysis of the methods. The numerical experiments illuminate that the method can be explicit, highly accurate, divergence-free in numerical terms, and of good long-term behavior.

对于三次域各向同性均匀介质麦克斯韦方程组，由于源场边界条件和源的多样性，目前几乎没有能够解决源场各种边界条件下所有问题的方法。幸运的是，在本文中，我们成功地给出了一类统一的方法（称为S-ERKN方法）来解决源场中各种边界条件下的问题。首先，我们对空间离散化进行了详细的研究，以得到所谓的半离散系统。在这里，我们得出结论，边界条件对微分矩阵（在本文中表示为LU）有意料之外的影响，但对半离散系统的扰动项（在本文中表示为F * U）有意想不到的影响。其次，我们选择了ERKN （Extended Runge-Kutta Nystrom）方法作为时间求解器，改善了许多传统数值解中通常限于2阶的时间阶数。为了使S-ERKN方法（由上文所示的时空离散化得到）易于低成本编码，我们研究了作为该方法基本计算单元的矩阵向量积LUV的快速计算。本文还对这些方法进行了发散性分析。数值实验表明，该方法清晰、精度高、无发散、长期性能好。

{"title":"S-ERKN methods solving Maxwell’s equations in source field under wide range of boundary conditions","authors":"Hongli Yang , Xianyang Zeng , Hao Yu","doi":"10.1016/j.matcom.2026.01.017","DOIUrl":"10.1016/j.matcom.2026.01.017","url":null,"abstract":"<div><div>For Maxwell’s equations for isotropic homogeneous media in a cubic domain, there have been few methods that can solve almost all problems under various boundary conditions in source field since the boundary conditions and the sources are diverse, by now. Fortunately, in this paper, we succeeded in giving a unified class of methods (called S-ERKN methods) that solve problems under a wide range of boundary conditions in source field. At first, we gave a detailed study on the spatial discretization to have a so-called semi-discrete system. Here we concluded that the boundary conditions had an unsurprising impact on the differentiation matrix (denoted as <span><math><msub><mrow><mi>L</mi></mrow><mrow><mi>U</mi></mrow></msub></math></span> in this paper) but had an unexpected effect on the perturbation term (denoted as <span><math><msub><mrow><mover><mrow><mi>F</mi></mrow><mrow><mo>̃</mo></mrow></mover></mrow><mrow><mi>U</mi></mrow></msub></math></span> in this paper) of the semi-discrete system. Secondly, we chose the ERKN (Extended Runge–Kutta Nystrom) methods as the temporal solver to improve the temporal order which is normally limited to 2 in many traditional numerical solutions. To make the S-ERKN method (obtained by the spatial and temporal discretization shown above) easy to code at low cost, we studied the fast calculation of the matrix vector product <span><math><mrow><msub><mrow><mi>L</mi></mrow><mrow><mi>U</mi></mrow></msub><mi>V</mi></mrow></math></span>, which is the basic computational unit of the method. In this paper, we also performed the divergence analysis of the methods. The numerical experiments illuminate that the method can be explicit, highly accurate, divergence-free in numerical terms, and of good long-term behavior.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"245 ","pages":"Pages 143-175"},"PeriodicalIF":4.4,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146038827","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}

引用次数: 0

FEM-MsFEM for an interface-coupled parabolic problem 界面耦合抛物问题的FEM-MsFEM

IF 4.4 2区数学 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Mathematics and Computers in Simulation

Pub Date : 2026-07-01 Epub Date: 2026-01-20 DOI: 10.1016/j.matcom.2026.01.023

Jiaping Yu , Wenhan Zhang , Ren Zhao , Haibiao Zheng

In this paper, we propose and analyze a finite element coupled multiscale finite element method (FEM-MsFEM) for an interface-coupled parabolic problem. The problem involves a coefficient with multiscale characteristics in one region and in the other region without such feature. Our algorithm consists of two main steps: first, solving for the multiscale basis functions in the multiscale region via parallel computation; and second, decoupling the interface-coupled parabolic problem using a data-passing partitioned scheme. This approach allows for the problem to be solved on relatively coarse grids, thereby reducing computational costs. Under suitable assumptions for the multiscale coefficient, we establish the unconditional stability and provide error estimates for the algorithm. The effectiveness of our method is demonstrated through several numerical experiments.

本文提出并分析了一种求解界面耦合抛物问题的有限元耦合多尺度有限元方法。该问题涉及一个区域具有多尺度特征的系数，而在另一个区域不具有多尺度特征的系数。该算法主要包括两个步骤：首先，通过并行计算求解多尺度区域内的多尺度基函数；其次，采用数据传递分区方案对接口耦合抛物问题进行解耦。这种方法允许在相对粗糙的网格上解决问题，从而减少计算成本。在适当的多尺度系数假设下，建立了算法的无条件稳定性，并给出了算法的误差估计。通过数值实验验证了该方法的有效性。

引用次数: 0

Cooperative and robust object manipulation by multiple robots via linear estimated state feedback 基于线性估计状态反馈的多机器人协同鲁棒目标操作

IF 4.4 2区数学 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Mathematics and Computers in Simulation

Pub Date : 2026-07-01 Epub Date: 2026-01-12 DOI: 10.1016/j.matcom.2026.01.009

Saleh Mobayen , Alireza Izadbakhsh

In modern industrial automation, the deployment of multiple robotic manipulators for cooperative operations has become increasingly common, offering enhanced system flexibility and responsiveness. However, as the number of manipulators increases, the system dynamics become substantially more nonlinear and complex, giving rise to unmodeled dynamics and various sources of uncertainty. Moreover, external disturbances can further degrade control performance, while the lack of a comprehensive sensing infrastructure may result in incomplete state information. To address these challenges, this study proposes a robust, model-independent control framework based on function approximation techniques. The methodology leverages linear differential equations with unknown coefficients to capture the aggregated system uncertainties under the assumption that such uncertainties can be effectively described using this structure. The approximation capability of the proposed model is then justified via the Stone-Weierstrass theorem, establishing the role of linear differential equations as universal approximators. Notably, the control strategy does not require velocity measurements, thereby simplifying its practical implementation. Stability analysis based on Lyapunov’s direct method ensures that tracking errors remain uniformly ultimately bounded. The controller is validated within a dual-arm cooperative manipulation scenario involving a rigid object, and its performance is benchmarked against three contemporary approximation-based control methods. Simulation results confirm the efficacy and robustness of the proposed approach.

在现代工业自动化中，部署多个机器人机械手进行协作操作已经变得越来越普遍，从而提高了系统的灵活性和响应能力。然而，随着机械臂数量的增加，系统动力学变得更加非线性和复杂，产生了未建模的动力学和各种不确定性来源。此外，外部干扰会进一步降低控制性能，而缺乏全面的传感基础设施可能导致状态信息不完整。为了解决这些挑战，本研究提出了一种基于函数逼近技术的鲁棒、模型无关的控制框架。该方法利用具有未知系数的线性微分方程来捕获聚合系统的不确定性，假设这种不确定性可以使用该结构有效地描述。然后通过Stone-Weierstrass定理证明了所提出模型的近似能力，建立了线性微分方程作为通用近似器的作用。值得注意的是，该控制策略不需要速度测量，从而简化了其实际实现。基于Lyapunov直接法的稳定性分析保证了跟踪误差最终保持一致有界。该控制器在涉及刚性物体的双臂协作操作场景中进行了验证，并与三种现代基于近似的控制方法进行了性能基准测试。仿真结果验证了该方法的有效性和鲁棒性。

{"title":"Cooperative and robust object manipulation by multiple robots via linear estimated state feedback","authors":"Saleh Mobayen , Alireza Izadbakhsh","doi":"10.1016/j.matcom.2026.01.009","DOIUrl":"10.1016/j.matcom.2026.01.009","url":null,"abstract":"<div><div>In modern industrial automation, the deployment of multiple robotic manipulators for cooperative operations has become increasingly common, offering enhanced system flexibility and responsiveness. However, as the number of manipulators increases, the system dynamics become substantially more nonlinear and complex, giving rise to unmodeled dynamics and various sources of uncertainty. Moreover, external disturbances can further degrade control performance, while the lack of a comprehensive sensing infrastructure may result in incomplete state information. To address these challenges, this study proposes a robust, model-independent control framework based on function approximation techniques. The methodology leverages linear differential equations with unknown coefficients to capture the aggregated system uncertainties under the assumption that such uncertainties can be effectively described using this structure. The approximation capability of the proposed model is then justified via the Stone-Weierstrass theorem, establishing the role of linear differential equations as universal approximators. Notably, the control strategy does not require velocity measurements, thereby simplifying its practical implementation. Stability analysis based on Lyapunov’s direct method ensures that tracking errors remain uniformly ultimately bounded. The controller is validated within a dual-arm cooperative manipulation scenario involving a rigid object, and its performance is benchmarked against three contemporary approximation-based control methods. Simulation results confirm the efficacy and robustness of the proposed approach.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"245 ","pages":"Pages 384-408"},"PeriodicalIF":4.4,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146078787","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}

引用次数: 0

下一页尾页

类型

全部化学•材料生命科学医学物理工程技术环境•农林材料科学地球科学法学管理学化学环境科学与生态学计算机科学教育学经济学农林科学人文科学生物学数学物理与天体物理心理学综合性期刊其他工业工程理学历史学农学文学信息工程

数据库

全部 ACS Publications Elsevier ieeexplore Springer The Royal Society of Chemistry Wiley

期刊

Mathematics and Computers in Simulation

全部 Acc. Chem. Res. ACS Applied Bio Materials ACS Appl. Electron. Mater. ACS Appl. Energy Mater. ACS Appl. Mater. Interfaces ACS Appl. Nano Mater. ACS Appl. Polym. Mater. ACS BIOMATER-SCI ENG ACS Catal. ACS Cent. Sci. ACS Chem. Biol. ACS Chemical Health & Safety ACS Chem. Neurosci. ACS Comb. Sci. ACS Earth Space Chem. ACS Energy Lett. ACS Infect. Dis. ACS Macro Lett. ACS Mater. Lett. ACS Med. Chem. Lett. ACS Nano ACS Omega ACS Photonics ACS Sens. ACS Sustainable Chem. Eng. ACS Synth. Biol. Anal. Chem. BIOCHEMISTRY-US Bioconjugate Chem. BIOMACROMOLECULES Chem. Res. Toxicol. Chem. Rev. Chem. Mater. CRYST GROWTH DES ENERG FUEL Environ. Sci. Technol. Environ. Sci. Technol. Lett. Eur. J. Inorg. Chem. IND ENG CHEM RES Inorg. Chem. J. Agric. Food. Chem. J. Chem. Eng. Data J. Chem. Educ. J. Chem. Inf. Model. J. Chem. Theory Comput. J. Med. Chem. J. Nat. Prod. J PROTEOME RES J. Am. Chem. Soc. LANGMUIR MACROMOLECULES Mol. Pharmaceutics Nano Lett. Org. Lett. ORG PROCESS RES DEV ORGANOMETALLICS J. Org. Chem. J. Phys. Chem. J. Phys. Chem. A J. Phys. Chem. B J. Phys. Chem. C J. Phys. Chem. Lett. Analyst Anal. Methods Biomater. Sci. Catal. Sci. Technol. Chem. Commun. Chem. Soc. Rev. CHEM EDUC RES PRACT CRYSTENGCOMM Dalton Trans. Energy Environ. Sci. ENVIRON SCI-NANO ENVIRON SCI-PROC IMP ENVIRON SCI-WAT RES Faraday Discuss. Food Funct. Green Chem. Inorg. Chem. Front. Integr. Biol. J. Anal. At. Spectrom. J. Mater. Chem. A J. Mater. Chem. B J. Mater. Chem. C Lab Chip Mater. Chem. Front. Mater. Horiz. MEDCHEMCOMM Metallomics Mol. Biosyst. Mol. Syst. Des. Eng. Nanoscale Nanoscale Horiz. Nat. Prod. Rep. New J. Chem. Org. Biomol. Chem. Org. Chem. Front. PHOTOCH PHOTOBIO SCI PCCP Polym. Chem.

﹀