Mathematics and Computers in Simulation最新文献_第8页

A fixed point evolution algorithm based on expanded Aitken rapid iteration method for global numeric optimization 基于扩展艾特肯快速迭代法的定点进化算法，用于全局数值优化

IF 4.4 2区数学

Mathematics and Computers in Simulation Pub Date : 2024-09-01 DOI: 10.1016/j.matcom.2024.08.027

Qian Zhang, Zhongbo Hu, Nan Hong, Qinghua Su

{"title":"A fixed point evolution algorithm based on expanded Aitken rapid iteration method for global numeric optimization","authors":"Qian Zhang, Zhongbo Hu, Nan Hong, Qinghua Su","doi":"10.1016/j.matcom.2024.08.027","DOIUrl":"10.1016/j.matcom.2024.08.027","url":null,"abstract":"<div><div>Evolution algorithms based on mathematical models whose reproduction operators are derived from mathematical models are a promising branch of metaheuristic algorithms. Aitken rapid iteration method, as a fixed point iteration technique for solving nonlinear equations, performs a procedure of progressive display of a root and generates an iterative sequence that exhibits a convergent trend. Inspired by the idea that an iterative sequence gradually converges to the optimal point during the progressive display procedure of a fixed point of an equation, a fixed point evolution algorithm based on the expanded Aitken rapid iteration method (FPEea) is proposed. To develop FPEea, an expanded Aitken rapid model is first constructed. Then, three polynomials which are derived from the expanded Aitken rapid model are used as the reproduction operator of FPEea to produce offspring. The performance of FPEea is investigated on CEC2019 and CEC2020 benchmark function sets, as well as four engineering design problems. Experimental results show that FPEea is an effective and competitive algorithm compared with several classical evolution algorithms and state-of-the-art algorithms.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":null,"pages":null},"PeriodicalIF":4.4,"publicationDate":"2024-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142418192","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

Global dynamics and numerical simulation of a modified epidemiological model for viral marketing on social networks 社交网络病毒式营销的改良流行病学模型的全局动态和数值模拟

IF 4.4 2区数学

Mathematics and Computers in Simulation Pub Date : 2024-08-31 DOI: 10.1016/j.matcom.2024.08.024

Manh Tuan Hoang , Hoai Thu Pham

{"title":"Global dynamics and numerical simulation of a modified epidemiological model for viral marketing on social networks","authors":"Manh Tuan Hoang , Hoai Thu Pham","doi":"10.1016/j.matcom.2024.08.024","DOIUrl":"10.1016/j.matcom.2024.08.024","url":null,"abstract":"<div><p>The aim of this work is to conduct a rigorous mathematical analysis for global dynamics and numerical simulation of a recognized viral marketing (VM) model, which is described by a system of ordinary differential equations (ODEs). We first establish positivity and boundedness of solutions and then investigate local and global asymptotic stability properties of possible equilibrium points. As an important consequence, complex dynamics of the VM model is determined fully.</p><p>Secondly, we develop the Mickens’ methodology to design a nonstandard finite difference (NSFD) scheme, which is useful in numerical simulation of the VM model. The main advantage of the constructed NSFD scheme is that it has the ability to preserve important mathematical features of the continuous-time model for all finite values of the step size. These features include the positivity and boundedness of solutions, positively invariant sets, equilibrium points and their asymptotic stability properties. Consequently, the NSFD scheme is not only effective to simulate dynamics of the VM model, but also easy to be implemented.</p><p>Thirdly, to emphasize implications of the constructed mathematical analysis, an extended version combining the integer-order ODE model under consideration with the Caputo fractional derivative is considered and analyzed. From the mathematical analysis performed for the integer-order VM model, global dynamics of the fractional-order VM model is also investigated rigorously.</p><p>Finally, the theoretical insights are supported by a set of illustrative numerical experiments.</p><p>The findings of this research not only improve some existing results in the literature, but may also provide several useful real-life applications.</p></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":null,"pages":null},"PeriodicalIF":4.4,"publicationDate":"2024-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142162808","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

Inner loop model predictive control and outer loop PI reference governor for PMSMs with input and state saturation for torque control 内环模型预测控制和外环 PI 参考调速器，用于具有输入和状态饱和的 PMSM 扭矩控制

IF 4.4 2区数学

Mathematics and Computers in Simulation Pub Date : 2024-08-31 DOI: 10.1016/j.matcom.2024.08.006

Tanja Zwerger , Paolo Mercorelli

{"title":"Inner loop model predictive control and outer loop PI reference governor for PMSMs with input and state saturation for torque control","authors":"Tanja Zwerger , Paolo Mercorelli","doi":"10.1016/j.matcom.2024.08.006","DOIUrl":"10.1016/j.matcom.2024.08.006","url":null,"abstract":"<div><p>This contribution considers a torque control scheme consisting of model predictive control (MPC) in the inner control loop together with PI reference governor in the outer control loop and a decoupling feedforward control for an isotropic permanent magnet synchronous machine (PMSM). This innovative approach is known in literature as PI-MPC dual loop control. A particular emphasis is given to the control governor strategy which is the outer loop PI reference governor and allows to regulate the machine in the flux weakening region and is therefore only active for field weakening. In this context the analysis of the stability based on Lyapunov’ approach of the control loop in flux weakening region is shown. The desired currents represent the reference currents for the MPC, which forms the inner control loop. The MPC is adapted using an extended Kalman filter (EKF), which estimates inductance of the electrical system in <span><math><mrow><mi>d</mi><mi>q</mi></mrow></math></span> coordinates by using a bivariate polynomial. Compared measurements with a hardware-in-the-loop (HIL) system show the effectiveness of the proposed control scheme with respect to a standard PI controller in inner loop (PI-PI scheme) in the presence of saturated inputs and state of a PMSM. The proposed MPC uses just an optimal, proportional control and thus avoids windup effects. Measurement results in the presence of input and state saturations show that MPC is working without overshoot in the currents which leads to less needed power in input.</p></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":null,"pages":null},"PeriodicalIF":4.4,"publicationDate":"2024-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0378475424003082/pdfft?md5=22b1f02acafad37d2142c8fc049c7498&pid=1-s2.0-S0378475424003082-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142151375","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Uniform convergence of finite element method on Bakhvalov-type mesh for a 2-D singularly perturbed convection–diffusion problem with exponential layers 巴赫瓦洛夫型网格上的有限元法对指数层的二维奇异扰动对流扩散问题的均匀收敛性

IF 4.4 2区数学

Mathematics and Computers in Simulation Pub Date : 2024-08-30 DOI: 10.1016/j.matcom.2024.08.032

Jin Zhang, Chunxiao Zhang

{"title":"Uniform convergence of finite element method on Bakhvalov-type mesh for a 2-D singularly perturbed convection–diffusion problem with exponential layers","authors":"Jin Zhang, Chunxiao Zhang","doi":"10.1016/j.matcom.2024.08.032","DOIUrl":"10.1016/j.matcom.2024.08.032","url":null,"abstract":"<div><p>Analyzing uniform convergence of finite element method for a 2-D singularly perturbed convection–diffusion problem with exponential layers on Bakhvalov-type mesh remains a complex, unsolved problem. Previous attempts to address this issue have encountered significant obstacles, largely due to the constraints imposed by a specific mesh. These difficulties stem from three primary factors: the width of the mesh subdomain adjacent to the transition point, constraints imposed by the Dirichlet boundary condition, and the structural characteristics of exponential layers. In response to these challenges, this paper introduces a novel analysis technique that leverages the properties of interpolation and the relationship between the smooth function and the layer function on the boundary. By combining this technique with a simplified interpolation, we establish the uniform convergence of optimal order <span><math><mi>k</mi></math></span> under an energy norm for finite element method of any order <span><math><mi>k</mi></math></span>. Numerical experiments validate our theoretical findings.</p></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":null,"pages":null},"PeriodicalIF":4.4,"publicationDate":"2024-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142122036","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

Local spline refinement driven by fault jump estimates for scattered data approximation 由故障跳变估计驱动的局部样条细化，用于散点数据逼近

IF 4.4 2区数学

Mathematics and Computers in Simulation Pub Date : 2024-08-30 DOI: 10.1016/j.matcom.2024.08.031

Cesare Bracco, Carlotta Giannelli, Francesco Patrizi, Alessandra Sestini

{"title":"Local spline refinement driven by fault jump estimates for scattered data approximation","authors":"Cesare Bracco, Carlotta Giannelli, Francesco Patrizi, Alessandra Sestini","doi":"10.1016/j.matcom.2024.08.031","DOIUrl":"10.1016/j.matcom.2024.08.031","url":null,"abstract":"<div><p>We present new fault jump estimates to guide local refinement in surface approximation schemes with adaptive spline constructions. The proposed approach is based on the idea that, since discontinuities in the data should naturally correspond to sharp variations in the reconstructed surface, the location and size of jumps detected in the input point cloud should drive the mesh refinement algorithm. To exploit the possibility of inserting local meshlines in one or the other coordinate direction, as suggested by the jump estimates, we propose a quasi-interpolation (QI) scheme based on locally refined B-splines (LR B-splines). Particular attention is devoted to the construction of the local operator of the LR B-spline QI scheme, which properly adapts the spline approximation according to the nature and density of the scattered data configuration. A selection of numerical examples outlines the performance of the method on synthetic and real datasets characterized by different geographical features.</p></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":null,"pages":null},"PeriodicalIF":4.4,"publicationDate":"2024-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0378475424003422/pdfft?md5=87f4c23744a6b643de8db4f53eff35f7&pid=1-s2.0-S0378475424003422-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142151379","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Stabilization for a class of fractional-order nonlinear reaction–diffusion systems with time-varying delay: Event-triggered boundary control approach 一类具有时变延迟的分数阶非线性反应-扩散系统的稳定：事件触发边界控制方法

IF 4.4 2区数学

Mathematics and Computers in Simulation Pub Date : 2024-08-30 DOI: 10.1016/j.matcom.2024.08.026

Ailiang Zhao , Junmin Li , Aili Fan

引用次数: 0

An efficient recursive technique with Padé approximation for a kind of Lane–Emden type equations emerging in various physical phenomena 针对各种物理现象中出现的一种 Lane-Emden 型方程的帕代近似高效递推技术

IF 4.4 2区数学

Mathematics and Computers in Simulation Pub Date : 2024-08-30 DOI: 10.1016/j.matcom.2024.08.025

Jyoti , Mandeep Singh

{"title":"An efficient recursive technique with Padé approximation for a kind of Lane–Emden type equations emerging in various physical phenomena","authors":"Jyoti , Mandeep Singh","doi":"10.1016/j.matcom.2024.08.025","DOIUrl":"10.1016/j.matcom.2024.08.025","url":null,"abstract":"<div><p>The study numerically examined a class of nonlinear singular differential problems known as the Lane–Emden differential equation, which emerges in numerous real-world situations. The primary goal of this work is to formulate a computationally efficient iterative technique for solving the nonlinear Lane–Emden initial value problems. The proposed approach is a hybrid of the homotopy perturbation method and the Padé approximation. The nonlinear singular Lane–Emden initial value problem (SLEIVP) is transformed into an equivalent recursive integral employing the Picard’s approach. To resolve the singularity and nonlinearity, the recursive integral equation is transformed into a system of integral equations by using the homotopy notion. Furthermore, to enhance the convergence rate of the technique, Padé approximation is taken into account. The convergence analysis for the proposed approach is also conducted. The present technique is tested on SLEIVPs and numerical findings are compared with the existing techniques, to demonstrate the accuracy, effectiveness and ease of use.</p></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":null,"pages":null},"PeriodicalIF":4.4,"publicationDate":"2024-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142096964","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

Linear quadratic optimal control of stochastic 2-D Roesser models 随机 2-D Roesser 模型的线性二次优化控制

IF 4.4 2区数学

Mathematics and Computers in Simulation Pub Date : 2024-08-28 DOI: 10.1016/j.matcom.2024.08.029

Xiaomin Xue , Juanjuan Xu , Huanshui Zhang

引用次数: 0

Nonstandard finite difference schemes for some epidemic optimal control problems 某些流行病最优控制问题的非标准有限差分方案

IF 4.4 2区数学

Mathematics and Computers in Simulation Pub Date : 2024-08-26 DOI: 10.1016/j.matcom.2024.08.028

Arsène J. Ouemba Tassé , Vuyiswa B. Kubalasa , Berge Tsanou , Jean M.-S, Lubuma

{"title":"Nonstandard finite difference schemes for some epidemic optimal control problems","authors":"Arsène J. Ouemba Tassé , Vuyiswa B. Kubalasa , Berge Tsanou , Jean M.-S, Lubuma","doi":"10.1016/j.matcom.2024.08.028","DOIUrl":"10.1016/j.matcom.2024.08.028","url":null,"abstract":"<div><p>We construct and analyse nonstandard finite difference (NSFD) schemes for two epidemic optimal control problems. Firstly, we consider the well-known MSEIR system that can be used to model childhood diseases such as the measles, with the vaccination as a control intervention. The second optimal control problem is related to the 2014–2016 West Africa Ebola Virus Disease (EVD) outbreak, that came with the unprecedented challenge of the disease spreading simultaneously in three different countries, namely Guinea, Liberia and Sierra Leone, where it was difficult to control the considerable migrations and travels of people inbound and outbound. We develop an extended SEIRD metapopulation model modified by the addition of compartments of quarantined and isolated individuals. The control parameters are the exit screening of travelers and the vaccination of the susceptible individuals. For the two optimal control problems, we provide the results on: (i) the (global) stability of the disease-free and/or endemic equilibria of the state variable systems; (ii) the positivity and boundedness of solutions of the state variables systems; (iii) the existence, uniqueness and characterization of the optimal control solutions that minimizes the cost functional. On the other hand: (iv) we design Euler-based nonstandard finite difference versions of the Forward-Backward Sweep Method (NSFD-FBSM) that are dynamically consistent with the state variable systems; (v) we provide numerical simulations that support the theory and show the superiority of the nonstandard approach over the classical FBSM. The numerical simulations suggest that significantly increasing the coverage of the vaccine with its implementation for adults as well is essential if the recurrence of measles outbreaks is to be stopped in South Africa. They also show that the optimal control vaccination for the 2014-2016 EVD is more efficient than the exit screening intervention.</p></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":null,"pages":null},"PeriodicalIF":4.4,"publicationDate":"2024-08-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0378475424003380/pdfft?md5=f50008c0dfc8293cc8457555ebff0bcd&pid=1-s2.0-S0378475424003380-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142099471","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

A computational approach to extreme values and related hitting probabilities in level-dependent quasi-birth–death processes 依赖水平的准出生-死亡过程中极值和相关命中概率的计算方法

IF 4.4 2区数学

Mathematics and Computers in Simulation Pub Date : 2024-08-24 DOI: 10.1016/j.matcom.2024.08.019

A. Di Crescenzo , A. Gómez-Corral , D. Taipe

引用次数: 0