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Piecewise Spectral Collocation Method for Second Order Volterra Integro-Differential Equations with Nonvanishing Delay

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Advances in Applied Mathematics and Mechanics 2022年第6期14卷 1333-1356页

作者： Zhenrong Chen Yanping Chen Yunqing Huang School of Mathematical Sciences South China Normal UniversityGuangzhouGuangdong 510631China School of Mathematics and Computational Science Hunan Key Laboratory for Computation and Simulation in Science and EngineeringXiangtan UniversityXiangtanHunan 411105China

In this paper,the piecewise spectral-collocation method is used to solve the second-order Volterra integral differential equation with nonvanishing *** this collocation method,the main discontinuity point of the solution of the equation is used to divide the partitions to overcome the disturbance of the numerical error convergence caused by the main discontinuity of the solution of the *** approximation in the sense of integral is constructed in numerical format,and the convergence of the spectral collocation method in the sense of the L¥and L2 norm is proved by the Dirichlet *** the same time,the error convergence also meets the effect of spectral accuracy *** numerical experimental results are given at the end also verify the correctness of the theoretically proven results.

关键词： Second-order Volterra type integro-differential equation delay function piecewise spectral-collocation method.

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Free vibration exploration of axially functionally graded carbon nanotube-reinforced beams through an innovative perturbative methodology 3

Free vibration exploration of axially functionally graded ca...

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2024 3rd International Conference on Aerospace, Aerodynamics and Mechatronics engineering, AAME 2024

作者： Chen, Chen Zhou, Lilin Ye, Tianyu Li, Daokui College of Aerospace Science and Engineering National University of Defense Technology Hunan Changsha410073 China Hunan Key Laboratory of Intelligent Planning and Simulation for Aerospace Missions Hunan Changsha410073 China Aviation Engineering Institute Civil Aviation Flight University of China Sichuan Guanghan618307 China

Axially functionally graded (AFG) carbon nanotube-reinforced composite (CNTRC) emerges as a promising solution for tailoring the stiffness and strength of various beam-like structures. Applications range from optimizing the weight-to-strength ratio of airplane wings to fine-tuning the frequency of micro-beam sensors, and even alleviating stresses induced by centrifugal forces or temperature gradients in turbine blades. However, the challenge of solving variable coefficient partial differential equations (VCPDEs) arising from the axial material gradient limits conventional methods to numerical and simulation techniques. In this study, a novel perturbation approach (PA) customized for AFG-CNTRC is highlighted for solving the problem analytically, simply, and precisely. First, the vibration model of an AFG-CNTRC beam is established according to the Euler-Bernoulli theory (EBT). Second, the vibration governing equations are solved by the PA and the state space method (SSM) analytically. Finally, the adaptivity and accuracy of the PA are validated and the effects of carbon nanotubes (CNTs) distribution patterns are analyzed. It is found that increasing CNT content at either end will increase the natural frequency for symmetric boundary conditions (BCs). The frequency decreases with the degree of nonlinearity distribution of CNTs. The frequency under the C-F BC exhibits low sensitivity to parameter effects. © Published under licence by IOP Publishing Ltd.

关键词： State space methods

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αSetup-PCTL:An Adaptive Setup-Based Two-Level Preconditioner for Sequence of Linear Systems of Three-Temperature Energy Equations

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Communications in Computational Physics 2022年第10期32卷 1287-1309页

作者： Silu Huang Xiaoqiang Yue Xiaowen Xu Laboratory of Computational Physics Institute of Applied Physics and ComputationalMathematicsBeijing 100088China National Center for Applied Mathematics in Hunan Key Laboratory of Intelligent Computing and Information Processing of Ministry of EducationHunan Key Laboratory for Computation and Simulation in Science and EngineeringXiangtan UniversityXiangtan 411105China

The iterative solution of the sequence of linear systems arising from threetemperature(3-T)energy equations is an essential component in the numerical simulation of radiative hydrodynamic(RHD)***,due to the complicated application features of the RHD problems,solving 3-T linear systems with classical preconditioned iterative techniques is *** address this difficulty,a physicalvariable based coarsening two-level(PCTL)preconditioner has been proposed by dividing the fully coupled system into four individual easier-to-solve *** its nearly optimal complexity and robustness,the PCTL algorithm suffers from poor efficiency because of the overhead associatedwith the construction of setup phase and the solution of ***,the PCTL algorithm employs a fixed strategy for solving the sequence of 3-T linear systems,which completely ignores the dynamically and slowly changing features of these linear *** address these problems and to efficiently solve the sequence of 3-T linear systems,we propose an adaptive two-level preconditioner based on the PCTL algorithm,referred to as α*** adaptive strategies of the αSetup-PCTL algorithm are inspired by those of αSetup-AMG algorithm,which is an adaptive-setup-based AMG solver for sequence of sparse linear *** proposed αSetup-PCTL algorithm could adaptively employ the appropriate strategies for each linear system,and thus increase the overall *** results demonstrate that,for 36 linear systems,the αSetup-PCTL algorithm achieves an average speedup of 2.2,and a maximum speedup of 4.2 when compared to the PCTL algorithm.

关键词： Sequence of linear systems sparse linear solver preconditioning methods radiation hydrodynamics simulation

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TWO-GRID ALGORITHM OF H^(1)-GALERKIN MIXED FINITE ELEMENT METHODS FOR SEMILINEAR PARABOLIC INTEGRO-DIFFERENTIAL EQUATIONS

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Journal of Computational Mathematics 2022年第5期40卷 667-685页

作者： Tianliang Hou Chunmei Liu Chunlei Dai Luoping Chen Yin Yang School of Mathematics and Statistics Beihua UniversityJilin 132013China College of Science Hunan University of Science and EngineeringYongzhou 425199China School of Mathematics Southwest Jiaotong UniversityChengdu 611756China Hunan Key Laboratory for Computation and Simulation in Science and Engineering Key Laboratory of Intelligent Computing&Information Processing of Ministry of EducationSchool of Mathematics and Computational ScienceXiangtan UniversityXiangtan 411105China

In this paper,we present a two-grid discretization scheme for semilinear parabolic integro-differential equations by H1-Galerkin mixed finite element *** use the lowest order Raviart-Thomas mixed finite elements and continuous linear finite element for spatial discretization,and backward Euler scheme for temporal ***,a priori error estimates and some superclose properties are ***,a two-grid scheme is presented and its convergence is *** the proposed two-grid scheme,the solution of the nonlinear system on a fine grid is reduced to the solution of the nonlinear system on a much coarser grid and the solution of two symmetric and positive definite linear algebraic equations on the fine grid and the resulting solution still maintains optimal ***,a numerical experiment is implemented to verify theoretical results of the proposed *** theoretical and numerical results show that the two-grid method achieves the same convergence property as the one-grid method with the choice h=H^(2).

关键词： Semilinear parabolic integro-differential equations H^(1)-Galerkin mixed finite element method A priori error estimates Two-grid Superclose.

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Quorum sensing regulation methods and their effects on biofilm in biological waste treatment systems: A review

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Frontiers of Environmental science & engineering 2022年第7期16卷 47-59页

作者： Zhuqiu Sun Jinying Xi Chunping Yang Wenjie Cong Environmental Simulation and Pollution Control State Key Joint Laboratory School of EnvironmentTsinghua UniversityBeijing100084China State Environmental Protection Key Laboratory of Microorganism Application and Risk Control(SMARC) Beijing100084China Guangdong Provincial Key Laboratory of Petrochemical Pollution Processes and Control School of Environmental Science and EngineeringGuangdong University of Petrochemical TechnologyMaoming525099China College of Environmental Science and Engineering Hunan University and Key Laboratory of Environmental Biology and Pollution Control(Hunan University)Ministry of EducationChangsha410082China

Quorum sensing (QS) plays an important role in microbial aggregation control. Recently, the optimization of biological waste treatment systems by QS regulation gained an increasing attention. The effects of QS regulation on treatment performances and biofilm were frequently investigated. To understand the state of art of QS regulation, this review summarizes the methods of QS enhancement and QS inhibition in biological waste treatment systems. Typical QS enhancement methods include adding exogenous QS molecules, adding QS accelerants and cultivating QS bacteria, while typical QS inhibition methods include additions of quorum quenching (QQ) bacteria, QS-degrading enzymes, QS-degrading oxidants, and QS inhibitors. The specific improvements after applying these QS regulation methods in different treatment systems are concluded. In addition, the effects of QS regulation methods on biofilm in biological waste treatment systems are reviewed in terms of biofilm formation, extracellular polymeric substances production, microbial viability, and microbial community. In the end, the knowledge gaps in current researches are analyzed, and the requirements for future study are suggested.

关键词： Quorum sensing Biological waste treatment Biofilm formation

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Identifying possible lncRNA-disease associations based on deep learning and positive-unlabeled learning

Identifying possible lncRNA-disease associations based on de...

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2022 IEEE International Conference on Bioinformatics and Biomedicine, BIBM 2022

作者： Peng, Lihong Huang, Liangliang Lu, Yuankang Liu, Guangyi Chen, Min Han, Guosheng Hunan University of Technology School of Computer Science Zhuzhou China Xiangtan University Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan China

ISBN: (纸本)9781665468190

lncRNAs are involved in many biological processes, and their mutations and disorders are closely related to many diseases. Identification of LncRNA-Disease Associations (LDAs) helps us understand the pathogenesis of diseases and improve their diagnosis and treatment. However, experiments to determine LDAs are expensive, so it is essential to exploit effective computational methods to screen possible LDAs. In this study, we developed an LDA prediction model (LDA-DLPU) based on deep learning and positive-unlabeled (PU) learning. First, LDA-DLPU extracted features of lncRNAs and diseases based on singular value decomposition and regression model. Second, it selected negative LDAs based on PU learning and graph autoencoder. Finally, it classified unknown lncRNA-disease pairs based on deep neural network. LDA-DLPU obtained the best performance on two datasets. We predict that BCYRN1 and IFNG-AS1 may associate with leukemia. © 2022 IEEE.

关键词： Diseases

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A Numerical Algorithm for the Caputo Tempered Fractional Advection-Diffusion Equation

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Communications on Applied Mathematics and Computation 2021年第1期3卷 41-59页

作者： Wenhui Guan Xuenian Cao School of Mathematics and Computational Science Hunan Key Laboratory for Computation and Simulation in Science and EngineeringXiangtan UniversityXiangtan 411105Hunan ProvinceChina

By transforming the Caputo tempered fractional advection-diffusion equation into the Riemann–Liouville tempered fractional advection-diffusion equation,and then using the fractional-compact Grünwald–Letnikov tempered difference operator to approximate the Riemann–Liouville tempered fractional partial derivative,the fractional central difference operator to discritize the space Riesz fractional partial derivative,and the classical central difference formula to discretize the advection term,a numerical algorithm is constructed for solving the Caputo tempered fractional advection-diffusion *** stability and the convergence analysis of the numerical method are *** experiments show that the numerical method is effective.

关键词： Caputo tempered fractional advection-diffusion equation Fractional-compact Grünwald–Letnikov tempered Fractional central difference operator Stability Convergence

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Stability analysis of Runge-Kutta methods for nonlinear Volterra delay-integro-differential-algebraic equations

arXiv

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arXiv 2025年

作者： Wang, Gehao Yu, Yuexin Hunan Key Laboratory for Computation and Simulation in Science and Engineering School of Mathematics and Computational Science Xiangtan University Hunan Xiangtan411105 China

This paper is devoted to examining the stability of Runge-Kutta methods for solving stiff nonlinear Volterra delay-integro-differential-algebraic equations (DIDAEs) with constant delay. Hybrid numerical schemes combining Runge-Kutta methods and compound quadrature rules are analyzed for nonlinear stiff DIDAEs. Criteria for ensuring the global and asymptotic stability of the proposed schemes are established. Several numerical examples are provided to validate the theoretical findings. Copyright © 2025, The Authors. All rights reserved.

关键词： Runge Kutta methods

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The Mean Time to Absorption on Horizontal Partitioned Sierpinski Gasket Networks

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Analysis in Theory and Applications 2024年第1期40卷 1-21页

作者： Zhizhuo Zhang Bo Wu Zuguo Yu School of Mathematics Southeast UniversityNanjingJianagsu 211189China School of Applied Mathematics Nanjing University of Finance and EconomicsNanjingJiangsu 210023China Key Laboratory of Intelligent Computing and Information Processing of Ministry of Education and Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan UniversityXiangtanHunan 411105China

The random walk is one of the most basic dynamic properties of complex networks,which has gradually become a research hotspot in recent years due to its many applications in actual *** important characteristic of the random walk is the mean time to absorption,which plays an extremely important role in the study of topology,dynamics and practical application of complex *** the mean time to absorption on the regular iterative self-similar network models is an important way to explore the inﬂuence of self-similarity on the properties of random walks on the *** existing literatures have proved that even local self-similar structures can greatly affect the properties of random walks on the global network,but they have failed to prove whether these effects are related to the scale of these self-similar *** this article,we construct and study a class of Horizontal Par-titioned Sierpinski Gasket network model based on the classic Sierpinski gasket net-work,which is composed of local self-similar structures,and the scale of these structures will be controlled by the partition coefﬁcient ***,the analytical expressions and approximate expressions of the mean time to absorption on the network model are obtained,which prove that the size of the self-similar structure in the network will directly restrict the inﬂuence of the self-similar structure on the properties of random walks on the ***,we also analyzed the mean time to absorption of different absorption nodes on the network toﬁnd the location of the node with the highest absorption efﬁciency.

关键词： Mean time to absorption self-similar network Sierpinski Gasket

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Attitude and Orbit Control for Closely Observing Attitude-Dodging Target

Attitude and Orbit Control for Closely Observing Attitude-Do...

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International Conference on Guidance, Navigation and Control, ICGNC 2022

作者： Huang, Xuan Zhang, Jin Zhang, Hanyu Liu, Yuanhe College of Aerospace Science and Engineering National University of Defense Technology Changsha410072 China Hunan Key Laboratory of Intelligent Planning and Simulation for Aerospace Missions Changsha410072 China

ISBN: (纸本)9789811966125

Aiming at the situation that the non-cooperative spacecraft keeps the specific surface facing away from the active spacecraft through attitude dodging, the six-degree-of-freedom (6-DOF) attitude and orbit control of the active spacecraft for proximity observation is studied. Based on the relative orbit and attitude dynamics model, an orbit maneuver strategy is proposed, which uses the target's control time delay to fly around the target first at an accelerated angular rate and then at a constant angular rate. Then the desired attitude of the active spacecraft is designed, so as to realize continuous tracking observation of the specific surface of the target. A 6-DOF fly-around-observation hyperbolic-tangent sliding mode controller (HTSMC) considering unknown bounded disturbances is designed, and the stability of the HTSMC is proven. The simulations indicate that the fly-around observation strategy is reasonable and feasible, and the HTSMC has a short convergence time and high control accuracy. © 2023, The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.

关键词： Time delay

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