Mathematics and Computers in Simulation最新文献

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

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

{"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

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

{"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

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

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

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

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

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

{"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

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

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

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

{"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

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

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

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

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

{"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

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

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

{"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