Pub Date : 2025-01-23DOI: 10.1016/j.cnsns.2025.108631
Sania Qureshi , Amanullah Soomro , Ioannis K. Argyros , Krzysztof Gdawiec , Ali Akgül , Marwan Alquran
There are many different fields of study where nonlinear polynomial-based models arise and need to be solved, making the study of root-finding iterative solvers an important topic of research. Our goal was to use the two most significant fractional differential operators, Caputo and Riemann–Liouville, and an existing time-efficient three-step Newton-like iterative solver to address the growing interest in fractional calculus. The classical solver is preserved alongside a damping term created within it that tends to 1 as the fractional order approaches 1. The solvers’ local and semi-local convergence are investigated, and the stability trade-off with convergence speed is discussed at length. The suggested fractional-order solvers are tested on a number of nonlinear one-dimensional polynomial-based problems that come up in image processing, mechanical design, and civil engineering, such as beam deflection; and many more.
{"title":"Use of fractional calculus to avoid divergence in Newton-like solver for solving one-dimensional nonlinear polynomial-based models","authors":"Sania Qureshi , Amanullah Soomro , Ioannis K. Argyros , Krzysztof Gdawiec , Ali Akgül , Marwan Alquran","doi":"10.1016/j.cnsns.2025.108631","DOIUrl":"10.1016/j.cnsns.2025.108631","url":null,"abstract":"<div><div>There are many different fields of study where nonlinear polynomial-based models arise and need to be solved, making the study of root-finding iterative solvers an important topic of research. Our goal was to use the two most significant fractional differential operators, Caputo and Riemann–Liouville, and an existing time-efficient three-step Newton-like iterative solver to address the growing interest in fractional calculus. The classical solver is preserved alongside a damping term created within it that tends to 1 as the fractional order <span><math><mi>α</mi></math></span> approaches 1. The solvers’ local and semi-local convergence are investigated, and the stability trade-off with convergence speed is discussed at length. The suggested fractional-order solvers are tested on a number of nonlinear one-dimensional polynomial-based problems that come up in image processing, mechanical design, and civil engineering, such as beam deflection; and many more.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"143 ","pages":"Article 108631"},"PeriodicalIF":3.4,"publicationDate":"2025-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143057375","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}
Pub Date : 2025-01-22DOI: 10.1016/j.cnsns.2025.108625
Haiyan Xu , Carlos Alberto Santos , Mengyun Zhang , Zhigui Lin
In order to understand how nonlocal diffusion and pulse intervention affect dynamics of species, we focus on an age-structured nonlocal diffusion model in moving and heterogeneous environment, where nonlocal diffusion describes the long range dispersal of species itself and time-periodic harvesting pulse exacting on the adult reflects human intervention. A generalized principal eigenvalue involving harvesting rate used to identify the spreading and vanishing outcomes is firstly defined and the existence of the principal eigenvalue is given under some conditions. Subsequently, properties of the generalized principal eigenvalue and the principal eigenvalue related to harvesting rate and length of habitat interval are analyzed, respectively. The criteria to governing spreading or vanishing of the species are finally investigated, with sufficient conditions for spreading-vanishing established. Our results indicate that complexities can be induced by the internal long rang dispersal and expanding capacities of species, as well as external harvesting intervention of human. Specifically, appropriate harvesting rate and expanding capacities can even change the reciprocal outcomes of species from co-existence to co-extinction.
{"title":"On an age-structured model in moving boundaries: The effects of nonlocal diffusion and harvesting pulse","authors":"Haiyan Xu , Carlos Alberto Santos , Mengyun Zhang , Zhigui Lin","doi":"10.1016/j.cnsns.2025.108625","DOIUrl":"10.1016/j.cnsns.2025.108625","url":null,"abstract":"<div><div>In order to understand how nonlocal diffusion and pulse intervention affect dynamics of species, we focus on an age-structured nonlocal diffusion model in moving and heterogeneous environment, where nonlocal diffusion describes the long range dispersal of species itself and time-periodic harvesting pulse exacting on the adult reflects human intervention. A generalized principal eigenvalue involving harvesting rate used to identify the spreading and vanishing outcomes is firstly defined and the existence of the principal eigenvalue is given under some conditions. Subsequently, properties of the generalized principal eigenvalue and the principal eigenvalue related to harvesting rate and length of habitat interval are analyzed, respectively. The criteria to governing spreading or vanishing of the species are finally investigated, with sufficient conditions for spreading-vanishing established. Our results indicate that complexities can be induced by the internal long rang dispersal and expanding capacities of species, as well as external harvesting intervention of human. Specifically, appropriate harvesting rate and expanding capacities can even change the reciprocal outcomes of species from co-existence to co-extinction.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"143 ","pages":"Article 108625"},"PeriodicalIF":3.4,"publicationDate":"2025-01-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143057364","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}
Pub Date : 2025-01-22DOI: 10.1016/j.cnsns.2025.108626
Jinxin Dou , Zhenping Li , Muchuan Ding , Hongliang Yao , Tianzhi Yang
The electromagnetic excitation of the motor affects the vibration characteristics of the transmission system it drives. This study employs a curved beam-based nonlinear energy sink (CNES) as a suppression measure to reduce torsional vibrations in a multi-degree-of-freedom transmission system subjected to both electromagnetic and external excitations. An approximate expression for the electromagnetic excitation is established, and its influence on the inherent characteristics of the transmission system is analyzed. Next, the structure and principles of the CNES are introduced, followed by the development of a dynamic model for the transmission system that incorporates the proposed CNES. Building on these foundations, the energy transfer of the CNES under transient excitations is analyzed using an analytical method. Further numerical analysis is conducted to examine the displacement attenuation and energy dissipation of the transmission system with CNES installed. Furthermore, this study explores the influence of the electromagnetic excitation on the response characteristics of the system and numerically analyzes the vibration suppression performance of the CNES on steady-state responses. Finally, an experimental platform for the transmission system is established, and the suppression performance of the CNES is validated through experiments. The results indicate consistency between the experiments and simulations regarding the performance of the CNES. This study offers valuable insights into the suppression of multi-modal vibrations in transmission systems subjected to multi-source excitations.
{"title":"Modelling and vibration suppression of a transmission system with a curved beam-based nonlinear energy sink","authors":"Jinxin Dou , Zhenping Li , Muchuan Ding , Hongliang Yao , Tianzhi Yang","doi":"10.1016/j.cnsns.2025.108626","DOIUrl":"10.1016/j.cnsns.2025.108626","url":null,"abstract":"<div><div>The electromagnetic excitation of the motor affects the vibration characteristics of the transmission system it drives. This study employs a curved beam-based nonlinear energy sink (CNES) as a suppression measure to reduce torsional vibrations in a multi-degree-of-freedom transmission system subjected to both electromagnetic and external excitations. An approximate expression for the electromagnetic excitation is established, and its influence on the inherent characteristics of the transmission system is analyzed. Next, the structure and principles of the CNES are introduced, followed by the development of a dynamic model for the transmission system that incorporates the proposed CNES. Building on these foundations, the energy transfer of the CNES under transient excitations is analyzed using an analytical method. Further numerical analysis is conducted to examine the displacement attenuation and energy dissipation of the transmission system with CNES installed. Furthermore, this study explores the influence of the electromagnetic excitation on the response characteristics of the system and numerically analyzes the vibration suppression performance of the CNES on steady-state responses. Finally, an experimental platform for the transmission system is established, and the suppression performance of the CNES is validated through experiments. The results indicate consistency between the experiments and simulations regarding the performance of the CNES. This study offers valuable insights into the suppression of multi-modal vibrations in transmission systems subjected to multi-source excitations.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"143 ","pages":"Article 108626"},"PeriodicalIF":3.4,"publicationDate":"2025-01-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143021212","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}
The rational breathers (Akhmediev, Kuznetsov-Ma, Peregrine) through the modulation instability (MI) are excited in positive ion - negative ion collisional plasmas by means of analytical and computation. The dynamics of the modulated waves are modeled by a nonlinear Schrödinger type equation with a linear damping term that arises due to the ion-ion weak collision. Both the low and high frequency waves undergo MI in a certain parameter space (that depends on the mass and temperature of both the ions). The computation on the basis of experimental parameters reveal the formation of rational breathers on a finite background in PINI plasmas. The weak collisional dissipation delays the wave focusing process of the rational breathers and also enhance the amplitude of the second wave focusing in the Akhmediev breather dynamics.
{"title":"Modulated wave dynamics and excitation of rational breathers in positive ion–negative ion collisional plasmas","authors":"Debkumar Chakraborty , Biplab Maity , Samiran Ghosh","doi":"10.1016/j.cnsns.2025.108629","DOIUrl":"10.1016/j.cnsns.2025.108629","url":null,"abstract":"<div><div>The rational breathers (Akhmediev, Kuznetsov-Ma, Peregrine) through the modulation instability (MI) are excited in positive ion - negative ion collisional plasmas by means of analytical and computation. The dynamics of the modulated waves are modeled by a nonlinear Schrödinger type equation with a linear damping term that arises due to the ion-ion weak collision. Both the low and high frequency waves undergo MI in a certain parameter space (that depends on the mass and temperature of both the ions). The computation on the basis of experimental parameters reveal the formation of rational breathers on a finite background in PINI plasmas. The weak collisional dissipation delays the wave focusing process of the rational breathers and also enhance the amplitude of the second wave focusing in the Akhmediev breather dynamics.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"143 ","pages":"Article 108629"},"PeriodicalIF":3.4,"publicationDate":"2025-01-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143057365","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}
Pub Date : 2025-01-21DOI: 10.1016/j.cnsns.2025.108616
Yifan Wang, Wei Sun
This study focuses on an adaptive decentralized control problem for second-order large-scale interconnected nonlinear systems with uncertainties. The proposed control method is the first study of second-order large-scale systems using fully actuated system approach, considering that most real physical systems are second-order, whereas the existing literature on large-scale systems primarily considers first-order systems. By integrating the fully actuated system approach, decentralized control and adaptive technology, a novel controller is devised to ensure that the signals of the closed-loop system remain semiglobally uniformly ultimately bounded, and the tracking errors converge to a small neighborhood of zero. Finally, a numerical simulation example is presented to validate the effectiveness of the proposed control method.
{"title":"Adaptive decentralized control for second-order large-scale nonlinear systems via fully actuated system approach","authors":"Yifan Wang, Wei Sun","doi":"10.1016/j.cnsns.2025.108616","DOIUrl":"10.1016/j.cnsns.2025.108616","url":null,"abstract":"<div><div>This study focuses on an adaptive decentralized control problem for second-order large-scale interconnected nonlinear systems with uncertainties. The proposed control method is the first study of second-order large-scale systems using fully actuated system approach, considering that most real physical systems are second-order, whereas the existing literature on large-scale systems primarily considers first-order systems. By integrating the fully actuated system approach, decentralized control and adaptive technology, a novel controller is devised to ensure that the signals of the closed-loop system remain semiglobally uniformly ultimately bounded, and the tracking errors converge to a small neighborhood of zero. Finally, a numerical simulation example is presented to validate the effectiveness of the proposed control method.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"143 ","pages":"Article 108616"},"PeriodicalIF":3.4,"publicationDate":"2025-01-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143057370","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}
Pub Date : 2025-01-21DOI: 10.1016/j.cnsns.2025.108624
Yanping Qiu , Jun Cheng , Zhidong Zhou , Jinde Cao
This paper focuses on the distributed filter issue for a class of nonlinear systems under hybrid cyber-attacks, encompassing both deception attacks and denial of service (DoS) attacks with uncertain attack probabilities. In the sensor network, each filter estimates the output signals of the systems by dealing with the output measurements from the systems and the information received from its neighbors and each filter may receive the state estimation information affected by outliers from its neighbors, which is propagated based on the communication topology. With the purpose of mitigating the effects from channel noise during the signal transmission on filtering error systems (FES) and the potential anomalies’ impact in signal transmission caused by the hybrid cyber-attacks, a dynamic saturation function-based distributed filter is designed during the filtering process, whose saturation level is adaptively varying based on previous measurement errors. Through this approach and by utilizing Lyapunov-Krasovskii theory, sufficient conditions are established to ensure the stochastic stability (SS) of the FES and to achieve the predefined performance objectives. Finally, a practical model is presented to demonstrate the effectiveness and practicality of the designed distributed filter methodology.
{"title":"Distributed filtering for T-S fuzzy systems under cyber-attacks with time-varying saturation function","authors":"Yanping Qiu , Jun Cheng , Zhidong Zhou , Jinde Cao","doi":"10.1016/j.cnsns.2025.108624","DOIUrl":"10.1016/j.cnsns.2025.108624","url":null,"abstract":"<div><div>This paper focuses on the distributed filter issue for a class of nonlinear systems under hybrid cyber-attacks, encompassing both deception attacks and denial of service (DoS) attacks with uncertain attack probabilities. In the sensor network, each filter estimates the output signals of the systems by dealing with the output measurements from the systems and the information received from its neighbors and each filter may receive the state estimation information affected by outliers from its neighbors, which is propagated based on the communication topology. With the purpose of mitigating the effects from channel noise during the signal transmission on filtering error systems (FES) and the potential anomalies’ impact in signal transmission caused by the hybrid cyber-attacks, a dynamic saturation function-based distributed filter is designed during the filtering process, whose saturation level is adaptively varying based on previous measurement errors. Through this approach and by utilizing Lyapunov-Krasovskii theory, sufficient conditions are established to ensure the stochastic stability (SS) of the FES and to achieve the predefined <span><math><msub><mrow><mi>H</mi></mrow><mrow><mi>∞</mi></mrow></msub></math></span> performance objectives. Finally, a practical model is presented to demonstrate the effectiveness and practicality of the designed distributed filter methodology.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"143 ","pages":"Article 108624"},"PeriodicalIF":3.4,"publicationDate":"2025-01-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143057369","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}
Pub Date : 2025-01-21DOI: 10.1016/j.cnsns.2025.108640
Yuan Wei , Jia Guo , Xiangyan Chen
The performance and efficiency of the mechanical system usually depend on the coordination between the rotor and other mechanical components. Due to the sliding motion between the coupling teeth, investigating the instability of the rotor is essential. The action of the coupling can cause changes in the seal performance. The article establishes a nonlinear dynamic rotor model that considers the coupling of internal friction and labyrinth seal, which is a dimensionless treatment and seeks to use the numerical method. The study investigated the impact of various parameters such as axial pressure drops, seal clearance, and seal length. Exploring the change of rotor system stability under the coupling effect of internal friction and labyrinth seal. By combining time history, bifurcation, and axis center trajectory analyze the dynamic characteristics, motion state, and seal force. The results indicate that the rotor system's stability decreases as speed increases with increased vibration amplitude. The increase in axial pressure drop causes the rotor system motion bifurcation point to advance, but it can suppress the offset at the first-critical speed. The increase in seal length can improve the seal effect, but the unstable speed becomes advanced, and the system stability is reduced. This study considers multiple factors and provides theoretical support for the dynamic design of the rotor system.
{"title":"Nonlinear dynamics analysis of labyrinth seal-rotor system considering internal friction in coupling","authors":"Yuan Wei , Jia Guo , Xiangyan Chen","doi":"10.1016/j.cnsns.2025.108640","DOIUrl":"10.1016/j.cnsns.2025.108640","url":null,"abstract":"<div><div>The performance and efficiency of the mechanical system usually depend on the coordination between the rotor and other mechanical components. Due to the sliding motion between the coupling teeth, investigating the instability of the rotor is essential. The action of the coupling can cause changes in the seal performance. The article establishes a nonlinear dynamic rotor model that considers the coupling of internal friction and labyrinth seal, which is a dimensionless treatment and seeks to use the numerical method. The study investigated the impact of various parameters such as axial pressure drops, seal clearance, and seal length. Exploring the change of rotor system stability under the coupling effect of internal friction and labyrinth seal. By combining time history, bifurcation, and axis center trajectory analyze the dynamic characteristics, motion state, and seal force. The results indicate that the rotor system's stability decreases as speed increases with increased vibration amplitude. The increase in axial pressure drop causes the rotor system motion bifurcation point to advance, but it can suppress the offset at the first-critical speed. The increase in seal length can improve the seal effect, but the unstable speed becomes advanced, and the system stability is reduced. This study considers multiple factors and provides theoretical support for the dynamic design of the rotor system.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"143 ","pages":"Article 108640"},"PeriodicalIF":3.4,"publicationDate":"2025-01-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143057366","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}
Pub Date : 2025-01-21DOI: 10.1016/j.cnsns.2025.108639
Zhengqiu Xie , Kun Xie , Shuaishuai Ge , Zhigang Zhang , Ruizhi Shu , Rulong Tan , Wenbin Huang
In this paper, a novel spring-based nonlinear energy sink (SNES) is proposed for suppressing torsional vibrations in long-shaft rotor systems. The SNES functions by employing a piecewise linear stiffness, which is generated through the extrusion of springs. This mechanism provides the long-shaft rotor system with a restoring torque that can be characterized as a cubic nonlinear force. The paper details the design of the SNES structure and formulates a dynamic model of the SNES-rotor system. Numerical investigations are conducted to assess the vibration damping capacity of the SNES under both transient and steady-state excitations, revealing the nonlinear dynamic behavior of the rotor-SNES system. Furthermore, the effects of various parameters on system performance are examined. Experimental studies on the integrated system demonstrate that the rotor system coupled with the SNES dissipates energy 1.47 times faster than a system without the SNES during transient responses. In terms of steady-state responses, the SNES achieves a vibration suppression rate of up to 52.60% in experiments. These results demonstrate the effective suppression of torsional vibrations in the rotor system by the proposed SNES.
{"title":"A novel spring-based nonlinear energy sink for torsional vibration suppression of long-shafting rotor system","authors":"Zhengqiu Xie , Kun Xie , Shuaishuai Ge , Zhigang Zhang , Ruizhi Shu , Rulong Tan , Wenbin Huang","doi":"10.1016/j.cnsns.2025.108639","DOIUrl":"10.1016/j.cnsns.2025.108639","url":null,"abstract":"<div><div>In this paper, a novel spring-based nonlinear energy sink (SNES) is proposed for suppressing torsional vibrations in long-shaft rotor systems. The SNES functions by employing a piecewise linear stiffness, which is generated through the extrusion of springs. This mechanism provides the long-shaft rotor system with a restoring torque that can be characterized as a cubic nonlinear force. The paper details the design of the SNES structure and formulates a dynamic model of the SNES-rotor system. Numerical investigations are conducted to assess the vibration damping capacity of the SNES under both transient and steady-state excitations, revealing the nonlinear dynamic behavior of the rotor-SNES system. Furthermore, the effects of various parameters on system performance are examined. Experimental studies on the integrated system demonstrate that the rotor system coupled with the SNES dissipates energy 1.47 times faster than a system without the SNES during transient responses. In terms of steady-state responses, the SNES achieves a vibration suppression rate of up to 52.60% in experiments. These results demonstrate the effective suppression of torsional vibrations in the rotor system by the proposed SNES.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"143 ","pages":"Article 108639"},"PeriodicalIF":3.4,"publicationDate":"2025-01-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143057368","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}
Pub Date : 2025-01-20DOI: 10.1016/j.cnsns.2025.108627
Xiaochen Chu , Xiangyu Shi , Dongyang Shi
In this paper, we propose a backward Euler semi-implicit full discrete scheme for the time-dependent incompressible MHD equations and study the superconvergence behavior of the scheme. The spatial discretization is based on the bilinear-constant-bilinear elements for the velocity, pressure and magnetic fields, respectively, while the time discretization is based on the first-order backward Euler scheme. Firstly, we prove a new high accuracy estimation lemma related to the magnetic field, and prove the unconditional boundedness of numerical solutions in -norm by introducing a time-discrete auxiliary system. Then we derive the superclose estimates rigorously, which lead to the corresponding superconvergence results with assistance from interpolation post-processing techniques. In the end, we provide some numerical examples to verify the correctness of our theoretical analysis.
{"title":"Unconditional superconvergence analysis of low-order conforming mixed finite element method for time-dependent incompressible MHD equations","authors":"Xiaochen Chu , Xiangyu Shi , Dongyang Shi","doi":"10.1016/j.cnsns.2025.108627","DOIUrl":"10.1016/j.cnsns.2025.108627","url":null,"abstract":"<div><div>In this paper, we propose a backward Euler semi-implicit full discrete scheme for the time-dependent incompressible MHD equations and study the superconvergence behavior of the scheme. The spatial discretization is based on the bilinear-constant-bilinear elements for the velocity, pressure and magnetic fields, respectively, while the time discretization is based on the first-order backward Euler scheme. Firstly, we prove a new high accuracy estimation lemma related to the magnetic field, and prove the unconditional boundedness of numerical solutions in <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>∞</mi></mrow></msup></math></span>-norm by introducing a time-discrete auxiliary system. Then we derive the superclose estimates rigorously, which lead to the corresponding superconvergence results with assistance from interpolation post-processing techniques. In the end, we provide some numerical examples to verify the correctness of our theoretical analysis.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"143 ","pages":"Article 108627"},"PeriodicalIF":3.4,"publicationDate":"2025-01-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143057372","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}
Pub Date : 2025-01-20DOI: 10.1016/j.cnsns.2025.108622
Sun-Ho Choi , Dohyun Kwon , Hyowon Seo
We present a sufficient condition for asymptotic rendezvous of a Cucker-Smale type model on the unit sphere with an inter-particle bonding force. This second-order dynamical system includes a rotation operator defined on the surface of the three-dimensional unit sphere, and we derive an exponential decay estimate for the diameter of agent positions and demonstrate time-asymptotic flocking for a class of initial data. The sufficient condition for the initial data depends only on the communication rate and inter-particle bonding parameter, independent of the number of agents. The lack of momentum conservation and the presence of a curved space domain pose challenges in applying standard methodologies used in the original Cucker-Smale model. To address this and obtain a uniform position alignment estimate, we employ an energy dissipation property of this system and a transformation from the Cucker-Smale type flocking model into an inhomogeneous system in which the solution contains the position and velocity diameters. The coefficients of the transformed system are controlled by the communication rate and a uniform upper bound of velocities obtained by the energy dissipation.
{"title":"Uniform position alignment estimate of a spherical flocking model with inter-particle bonding forces","authors":"Sun-Ho Choi , Dohyun Kwon , Hyowon Seo","doi":"10.1016/j.cnsns.2025.108622","DOIUrl":"10.1016/j.cnsns.2025.108622","url":null,"abstract":"<div><div>We present a sufficient condition for asymptotic rendezvous of a Cucker-Smale type model on the unit sphere with an inter-particle bonding force. This second-order dynamical system includes a rotation operator defined on the surface of the three-dimensional unit sphere, and we derive an exponential decay estimate for the diameter of agent positions and demonstrate time-asymptotic flocking for a class of initial data. The sufficient condition for the initial data depends only on the communication rate and inter-particle bonding parameter, independent of the number of agents. The lack of momentum conservation and the presence of a curved space domain pose challenges in applying standard methodologies used in the original Cucker-Smale model. To address this and obtain a uniform position alignment estimate, we employ an energy dissipation property of this system and a transformation from the Cucker-Smale type flocking model into an inhomogeneous system in which the solution contains the position and velocity diameters. The coefficients of the transformed system are controlled by the communication rate and a uniform upper bound of velocities obtained by the energy dissipation.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"143 ","pages":"Article 108622"},"PeriodicalIF":3.4,"publicationDate":"2025-01-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143057373","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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