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Adaptive time-space resource and waveform control for collocated MIMO radar with simultaneous multi-beam 被引量:4
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作者 CHENG Ting LI Xi +1 位作者 TAN Qianqian SU Yang 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2022年第1期47-59,共13页
Collocated multiple input multiple output(MIMO)radar,which has agile multi-beam working mode,can offer enhanced multiple targets tracking(MTT)ability.In detail,it can illuminate different targets simultaneously with m... Collocated multiple input multiple output(MIMO)radar,which has agile multi-beam working mode,can offer enhanced multiple targets tracking(MTT)ability.In detail,it can illuminate different targets simultaneously with multi-beam or one wide beam among multi-beam,providing greater degree of freedom in system resource control.An adaptive time-space resource and waveform control optimization model for the collocated MIMO radar with simultaneous multi-beam is proposed in this paper.The aim of the proposed scheme is to improve the overall tracking accuracy and meanwhile minimize the resource consumption under the guarantee of effective targets detection.A resource and waveform control algorithm which integrates the genetic algorithm(GA)is proposed to solve the optimization problem.The optimal transmitting waveform parameters,system sampling period,sub-array number,binary radar tracking parameterχ_i(t_k),transmitting energy and multi-beam direction vector combination are chosen adaptively,where the first one realizes the waveform control and the latter five realize the timespace resource allocation.Simulation results demonstrate the effectiveness of the proposed control method. 展开更多
关键词 multiple targets tracking(MTT) collocated multiple input multiple output(MIMO)radar time-space resource allocation waveform control
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Antenna selection in MIMO radar with collocated antennas 被引量:3
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作者 ZHANG Haowei XIE Junwei +1 位作者 SHI Junpeng ZHANG Zhaojian 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2019年第6期1119-1131,共13页
An antenna adjustment strategy is developed for the target tracking problem in the collocated multiple-input multipleoutput(MIMO)radar.The basic technique of this strategy is to optimally allocate antennas by the prio... An antenna adjustment strategy is developed for the target tracking problem in the collocated multiple-input multipleoutput(MIMO)radar.The basic technique of this strategy is to optimally allocate antennas by the prior information in the tracking recursive period,with the objective of enhancing the worst-case estimate precision of multiple targets.On account of the posterior Cramer-Rao lower bound(PCRLB)offering a quantitative measure for target tracking accuracy,the PCRLB of joint direction-of-arrival(DOA)and Doppler is derived and utilized as the optimization criterion.It is shown that the dynamic antenna selection problem is NP-hard,and an efficient technique which combines convex relaxation with local search is put forward as the solution.Simulation results demonstrate the outperformance of the proposed strategy to the fixed antenna configuration and heuristic search algorithm.Moreover,it is able to offer close-to performance of the exhaustive search method. 展开更多
关键词 collocated multiple-input multiple-output(MIMO)radar multi-target tracking antenna selection posterior Cramer Rao lower bound(PCRLB) direction-of-arrival(DOA).
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THE FINITE VOLUME PROJECTION METHOD WITH HYBRID UNSTRUCTURED TRIANGULAR COLLOCATED GRIDS FOR INCOMPRESSIBLE FLOWS 被引量:8
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作者 GAO Wei DUAN Ya-li LIU Ru-xun 《Journal of Hydrodynamics》 SCIE EI CSCD 2009年第2期201-211,共11页
In this article a finite volume method is proposed to solve viscous incompressible Navier-Stokes equations in two-dimensional regions with corners and curved boundaries. A hybrid collocated-grid variable arrangement i... In this article a finite volume method is proposed to solve viscous incompressible Navier-Stokes equations in two-dimensional regions with corners and curved boundaries. A hybrid collocated-grid variable arrangement is adopted, in which the velocity and pressure are stored at the centroid and the circumcenters of the triangular control cell, respectively. The cell flux is defined at the mid-point of the cell face. Second-order implicit time integration schemes are used for convection and diffusion terms. The second-order upwind scheme is used for convection fluxes. The present method is validated by results of several viscous flows. 展开更多
关键词 incompressible viscous flows Navier-Stokes equations finite volume method projection method unstructured collocated grid
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Regularity for Euler-Bernoulli Equations with Boundary Control and Collocated Observation 被引量:2
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作者 WEN Ruili CHAI Shugen 《Journal of Systems Science & Complexity》 SCIE EI CSCD 2015年第4期788-798,共11页
This paper studies the regularity of Euler-Bernoulli equations on a bounded domain of Rn(n≥2)with boundary controls and collocated observations.The authors consider the Dirichlet controls in the case of hinged and cl... This paper studies the regularity of Euler-Bernoulli equations on a bounded domain of Rn(n≥2)with boundary controls and collocated observations.The authors consider the Dirichlet controls in the case of hinged and clamped boundary controls respectively.It is shown that the systems are regular in the sense of G.Weiss.The feedthrough operators are founded to be zero. 展开更多
关键词 Boundary control and collocated observation Euler-Bernoulli plate equation regularity.
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A Study on the Assessment and Integration of Multi-Source Evapotranspiration Products over the Tibetan Plateau
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作者 Ming CHENG Lei ZHONG +6 位作者 Yaoming MA Han MA Yaoxin CHANG Peizhen LI Meilin CHENG Xian WANG Nan GE 《Advances in Atmospheric Sciences》 SCIE CAS CSCD 2024年第3期435-448,共14页
Evapotranspiration(ET)is a crucial variable in the terrestrial water,carbon,and energy cycles.At present,a large number of multi source ET products exist.Due to sparse observations,however,great challenges exist in th... Evapotranspiration(ET)is a crucial variable in the terrestrial water,carbon,and energy cycles.At present,a large number of multi source ET products exist.Due to sparse observations,however,great challenges exist in the evaluation and integration of ET products in remote and complex areas such as the Tibetan Plateau(TP).In this paper,the applicability of the multiple collocation(MC)method over the TP is evaluated for the first time,and the uncertainty of multisource ET products(based on reanalysis,remote sensing,and land surface models)is further analyzed,which provides a theoretical basis for ET data fusion.The results show that 1)ET uncertainties quantified via the MC method are lower in RS-based ET products(5.95 vs.7.06 mm month^(-1))than in LSM ET products(10.22 vs.17.97 mm month^(-1))and reanalysis ET estimates(7.27 vs.12.26 mm month-1).2)A multisource evapotranspiration(MET)dataset is generated at a monthly temporal scale with a spatial resolution of 0.25°across the TP during 2005-15.MET has better performance than any individual product.3)Based on the fusion product,the total ET amount over the TP and its patterns of spatiotemporal variability are clearly identified.The annual total ET over the entire TP is approximately 380.60 mm.Additionally,an increasing trend of 1.59±0.85 mm yr^(-1)over the TP is shown during 2005-15.This study provides a basis for future studies on water and energy cycles and water resource management over the TP and surrounding regions. 展开更多
关键词 EVAPOTRANSPIRATION data fusion multiple collocation the Tibetan Plateau
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Review of Collocation Methods and Applications in Solving Science and Engineering Problems
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作者 Weiwu Jiang Xiaowei Gao 《Computer Modeling in Engineering & Sciences》 SCIE EI 2024年第7期41-76,共36页
The collocation method is a widely used numerical method for science and engineering problems governed by partial differential equations.This paper provides a comprehensive review of collocation methods and their appl... The collocation method is a widely used numerical method for science and engineering problems governed by partial differential equations.This paper provides a comprehensive review of collocation methods and their applications,focused on elasticity,heat conduction,electromagnetic field analysis,and fluid dynamics.The merits of the collocation method can be attributed to the need for element mesh,simple implementation,high computational efficiency,and ease in handling irregular domain problems since the collocation method is a type of node-based numerical method.Beginning with the fundamental principles of the collocation method,the discretization process in the continuous domain is elucidated,and how the collocation method approximation solutions for solving differential equations are explained.Delving into the historical development of the collocation methods,their earliest applications and key milestones are traced,thereby demonstrating their evolution within the realm of numerical computation.The mathematical foundations of collocation methods,encompassing the selection of interpolation functions,definition of weighting functions,and derivation of integration rules,are examined in detail,emphasizing their significance in comprehending the method’s effectiveness and stability.At last,the practical application of the collocation methods in engineering contexts is emphasized,including heat conduction simulations,electromagnetic coupled field analysis,and fluid dynamics simulations.These specific case studies can underscore collocation method’s broad applicability and effectiveness in addressing complex engineering challenges.In conclusion,this paper puts forward the future development trend of the collocation method through rigorous analysis and discussion,thereby facilitating further advancements in research and practical applications within these fields. 展开更多
关键词 Collocation method meshless method discrete schemes for functions numerical calculation
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A Novel Method for Linear Systems of Fractional Ordinary Differential Equations with Applications to Time-Fractional PDEs
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作者 Sergiy Reutskiy Yuhui Zhang +1 位作者 Jun Lu Ciren Pubu 《Computer Modeling in Engineering & Sciences》 SCIE EI 2024年第5期1583-1612,共30页
This paper presents an efficient numerical technique for solving multi-term linear systems of fractional ordinary differential equations(FODEs)which have been widely used in modeling various phenomena in engineering a... This paper presents an efficient numerical technique for solving multi-term linear systems of fractional ordinary differential equations(FODEs)which have been widely used in modeling various phenomena in engineering and science.An approximate solution of the system is sought in the formof the finite series over the Müntz polynomials.By using the collocation procedure in the time interval,one gets the linear algebraic system for the coefficient of the expansion which can be easily solved numerically by a standard procedure.This technique also serves as the basis for solving the time-fractional partial differential equations(PDEs).The modified radial basis functions are used for spatial approximation of the solution.The collocation in the solution domain transforms the equation into a system of fractional ordinary differential equations similar to the one mentioned above.Several examples have verified the performance of the proposed novel technique with high accuracy and efficiency. 展开更多
关键词 System of FODEs numerical solution Müntz polynomial basis time fractional PDE BSM collocation method
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A Collocation Technique via Pell-Lucas Polynomials to Solve Fractional Differential EquationModel for HIV/AIDS with Treatment Compartment
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作者 Gamze Yıldırım Suayip Yüzbası 《Computer Modeling in Engineering & Sciences》 SCIE EI 2024年第10期281-310,共30页
In this study,a numerical method based on the Pell-Lucas polynomials(PLPs)is developed to solve the fractional order HIV/AIDS epidemic model with a treatment compartment.The HIV/AIDS mathematical model with a treatmen... In this study,a numerical method based on the Pell-Lucas polynomials(PLPs)is developed to solve the fractional order HIV/AIDS epidemic model with a treatment compartment.The HIV/AIDS mathematical model with a treatment compartment is divided into five classes,namely,susceptible patients(S),HIV-positive individuals(I),individuals with full-blown AIDS but not receiving ARV treatment(A),individuals being treated(T),and individuals who have changed their sexual habits sufficiently(R).According to the method,by utilizing the PLPs and the collocation points,we convert the fractional order HIV/AIDS epidemic model with a treatment compartment into a nonlinear system of the algebraic equations.Also,the error analysis is presented for the Pell-Lucas approximation method.The aim of this study is to observe the behavior of five populations after 200 days when drug treatment is applied to HIV-infectious and full-blown AIDS people.To demonstrate the usefulness of this method,the applications are made on the numerical example with the help of MATLAB.In addition,four cases of the fractional order derivative(p=1,p=0.95,p=0.9,p=0.85)are examined in the range[0,200].Owing to applications,we figured out that the outcomes have quite decent errors.Also,we understand that the errors decrease when the value of N increases.The figures in this study are created in MATLAB.The outcomes indicate that the presented method is reasonably sufficient and correct. 展开更多
关键词 Collocation method fractional differential equations HIV/AIDS epidemic model Pell-Lucas polynomials
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AHermitian C^(2) Differential Reproducing Kernel Interpolation Meshless Method for the 3D Microstructure-Dependent Static Flexural Analysis of Simply Supported and Functionally Graded Microplates
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作者 Chih-Ping Wu Ruei-Syuan Chang 《Computer Modeling in Engineering & Sciences》 SCIE EI 2024年第10期917-949,共33页
This work develops a Hermitian C^(2) differential reproducing kernel interpolation meshless(DRKIM)method within the consistent couple stress theory(CCST)framework to study the three-dimensional(3D)microstructuredepend... This work develops a Hermitian C^(2) differential reproducing kernel interpolation meshless(DRKIM)method within the consistent couple stress theory(CCST)framework to study the three-dimensional(3D)microstructuredependent static flexural behavior of a functionally graded(FG)microplate subjected to mechanical loads and placed under full simple supports.In the formulation,we select the transverse stress and displacement components and their first-and second-order derivatives as primary variables.Then,we set up the differential reproducing conditions(DRCs)to obtain the shape functions of the Hermitian C^(2) differential reproducing kernel(DRK)interpolant’s derivatives without using direct differentiation.The interpolant’s shape function is combined with a primitive function that possesses Kronecker delta properties and an enrichment function that constituents DRCs.As a result,the primary variables and their first-and second-order derivatives satisfy the nodal interpolation properties.Subsequently,incorporating ourHermitianC^(2)DRKinterpolant intothe strong formof the3DCCST,we develop a DRKIM method to analyze the FG microplate’s 3D microstructure-dependent static flexural behavior.The Hermitian C^(2) DRKIM method is confirmed to be accurate and fast in its convergence rate by comparing the solutions it produces with the relevant 3D solutions available in the literature.Finally,the impact of essential factors on the transverse stresses,in-plane stresses,displacements,and couple stresses that are induced in the loaded microplate is examined.These factors include the length-to-thickness ratio,the material length-scale parameter,and the inhomogeneity index,which appear to be significant. 展开更多
关键词 Consistent/modified couple stress theory differential reproducing kernel methods microplates point collocation methods static flexural 3D microstructure-dependent analysis
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Effects of Collocational Congruency,Frequency and L2 Proficiency on the Processing of English Adjective-Noun Collocations
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作者 Lianrui YANG Qun ZHANG +1 位作者 Ni LI Ying CHEN 《Chinese Journal of Applied Linguistics》 2024年第3期393-413,524,共22页
The present study investigates the effects of congruency and frequency on adjective-noun collocational processing for Chinese learners of English at two proficiency levels based on the data obtained in an online accep... The present study investigates the effects of congruency and frequency on adjective-noun collocational processing for Chinese learners of English at two proficiency levels based on the data obtained in an online acceptability judgment task.The subject pool of this research included 60 English majors studying at a university in China;30 were selected as a higher-proficiency group and 30 as a lower-proficiency group according to their Vocabulary Levels Test(Schmitt et al.,2001)scores and their self-reported proficiency in English.The experimental materials were programmed to E-prime 2.0 and included six types of collocations:(1)15 high-frequency congruent collocations,(2)15 low-frequency congruent collocations,(3)15 high-frequency incongruent collocations,(4)15 low-frequency incongruent collocations,(5)15 Chinese-only items,and(6)75 unrelated items for baseline data.The collected response times(RTs)and accuracy rates data were statistically analyzed by the use of an ANOVA test and pairwise comparisons through SPSS 16.0 software.The results revealed that:(1)the adjective-noun collocational processing of Chinese English learners is influenced by collocational frequency,congruency and L2 proficiency;(2)the processing time is affected by the interaction of congruency and frequency;and(3)the interactive effect of L2 proficiency in conjunction with congruency and frequency also influences the processing quality. 展开更多
关键词 adjective-noun collocations congruency effects frequency effects L2 proficiency
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耦合拉格朗日-欧拉方法及其在海洋工程中的应用
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作者 钱志浩 杨腾茂 刘谋斌 《哈尔滨工程大学学报(英文版)》 CSCD 2024年第2期366-397,共32页
Combining the strengths of Lagrangian and Eulerian descriptions,the coupled Lagrangian–Eulerian methods play an increasingly important role in various subjects.This work reviews their development and application in o... Combining the strengths of Lagrangian and Eulerian descriptions,the coupled Lagrangian–Eulerian methods play an increasingly important role in various subjects.This work reviews their development and application in ocean engineering.Initially,we briefly outline the advantages and disadvantages of the Lagrangian and Eulerian descriptions and the main characteristics of the coupled Lagrangian–Eulerian approach.Then,following the developmental trajectory of these methods,the fundamental formulations and the frameworks of various approaches,including the arbitrary Lagrangian–Eulerian finite element method,the particle-in-cell method,the material point method,and the recently developed Lagrangian–Eulerian stabilized collocation method,are detailedly reviewed.In addition,the article reviews the research progress of these methods with applications in ocean hydrodynamics,focusing on free surface flows,numerical wave generation,wave overturning and breaking,interactions between waves and coastal structures,fluid–rigid body interactions,fluid–elastic body interactions,multiphase flow problems and visualization of ocean flows,etc.Furthermore,the latest research advancements in the numerical stability,accuracy,efficiency,and consistency of the coupled Lagrangian–Eulerian particle methods are reviewed;these advancements enable efficient and highly accurate simulation of complicated multiphysics problems in ocean and coastal engineering.By building on these works,the current challenges and future directions of the hybrid Lagrangian–Eulerian particle methods are summarized. 展开更多
关键词 Coupled Lagrangian–Eulerian description Ocean engineering Wave–structure interaction Particle methods Arbitrary Lagrangian–Eulerian(ALE)methods Particle-in-cell(PIC) Material point method(MPM) Lagrangian–Eulerian stabilized collocation method(LESCM)
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An Extended Numerical Method by Stancu Polynomials for Solution of Integro-Differential Equations Arising in Oscillating Magnetic Fields
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作者 Neşe İşler Acar 《Advances in Pure Mathematics》 2024年第10期785-796,共12页
In this study, the Bernstein collocation method has been expanded to Stancu collocation method for numerical solution of the charged particle motion for certain configurations of oscillating magnetic fields modelled b... In this study, the Bernstein collocation method has been expanded to Stancu collocation method for numerical solution of the charged particle motion for certain configurations of oscillating magnetic fields modelled by a class of linear integro-differential equations. As the method has been improved, the Stancu polynomials that are generalization of the Bernstein polynomials have been used. The method has been tested on a physical problem how the method can be applied. Moreover, numerical results of the method have been compared with the numerical results of the other methods to indicate the efficiency of the method. 展开更多
关键词 Stancu Polynomials Collocation Method Integro-Differential Equations Linear Equation Systems Matrix Equations
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New Perspective to Isogeometric Analysis:Solving Isogeometric Analysis Problem by Fitting Load Function 被引量:1
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作者 Jingwen Ren Hongwei Lin 《Computer Modeling in Engineering & Sciences》 SCIE EI 2023年第9期2957-2984,共28页
Isogeometric analysis(IGA)is introduced to establish the direct link between computer-aided design and analysis.It is commonly implemented by Galerkin formulations(isogeometric Galerkin,IGA-G)through the use of nonuni... Isogeometric analysis(IGA)is introduced to establish the direct link between computer-aided design and analysis.It is commonly implemented by Galerkin formulations(isogeometric Galerkin,IGA-G)through the use of nonuniform rational B-splines(NURBS)basis functions for geometric design and analysis.Another promising approach,isogeometric collocation(IGA-C),working directly with the strong form of the partial differential equation(PDE)over the physical domain defined by NURBS geometry,calculates the derivatives of the numerical solution at the chosen collocation points.In a typical IGA,the knot vector of the NURBS numerical solution is only determined by the physical domain.A new perspective on the IGAmethod is proposed in this study to improve the accuracy and convergence of the solution.Solving the PDE with IGA can be regarded as fitting the load function defined on the NURBS geometry(right-hand side)with derivatives of the NURBS numerical solution(left-hand side).Moreover,the design of the knot vector has a close relationship to theNURBS functions to be fitted in the area of data fitting in geometric design.Therefore,the detected feature points of the load function are integrated into the initial knot vector of the physical domainto construct thenewknot vector of thenumerical solution.Then,they are connected seamlessly with the IGA-C framework for its great potential combining the accuracy and smoothness merits with the computational efficiency,which we call isogeometric collocation by fitting load function(IGACL).In numerical experiments,we implement our method to solve 1D,2D,and 3D PDEs and demonstrate the improvement in accuracy by comparing it with the standard IGA-C method.We also verify the superiority in the accuracy of our knot selection scheme when employed in the IGA-G method,which we call isogeometric Galerkin by fitting load function(IGA-GL). 展开更多
关键词 Isogeometric analysis collocation methods feature point detection knot vector
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An Efficient Numerical Scheme for Biological Models in the Frame of Bernoulli Wavelets 被引量:1
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作者 Fei Li Haci Mehmet Baskonus +3 位作者 S.Kumbinarasaiah G.Manohara Wei Gao Esin Ilhan 《Computer Modeling in Engineering & Sciences》 SCIE EI 2023年第12期2381-2408,共28页
This article considers three types of biological systems:the dengue fever disease model,the COVID-19 virus model,and the transmission of Tuberculosis model.The new technique of creating the integration matrix for the ... This article considers three types of biological systems:the dengue fever disease model,the COVID-19 virus model,and the transmission of Tuberculosis model.The new technique of creating the integration matrix for the Bernoulli wavelets is applied.Also,the novel method proposed in this paper is called the Bernoulli wavelet collocation scheme(BWCM).All three models are in the form system of coupled ordinary differential equations without an exact solution.These systems are converted into a system of algebraic equations using the Bernoulli wavelet collocation scheme.The numerical wave distributions of these governing models are obtained by solving the algebraic equations via the Newton-Raphson method.The results obtained from the developed strategy are compared to several schemes such as the Runge Kutta method,and ND solver in mathematical software.The convergence analyses are discussed through theorems.The newly implemented Bernoulli wavelet method improves the accuracy and converges when it is compared with the existing methods in the literature. 展开更多
关键词 Biological systems system of coupled ODEs bernoulli wavelets functional matrix collocation technique
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A Numerical Investigation Based on Exponential Collocation Method for Nonlinear SITR Model of COVID-19 被引量:1
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作者 Mohammad Aslefallah Suayip Yüzbasi Saeid Abbasbandy 《Computer Modeling in Engineering & Sciences》 SCIE EI 2023年第8期1687-1706,共20页
In this work,the exponential approximation is used for the numerical simulation of a nonlinear SITR model as a system of differential equations that shows the dynamics of the new coronavirus(COVID-19).The SITR mathema... In this work,the exponential approximation is used for the numerical simulation of a nonlinear SITR model as a system of differential equations that shows the dynamics of the new coronavirus(COVID-19).The SITR mathematical model is divided into four classes using fractal parameters for COVID-19 dynamics,namely,susceptible(S),infected(I),treatment(T),and recovered(R).The main idea of the presented method is based on the matrix representations of the exponential functions and their derivatives using collocation points.To indicate the usefulness of this method,we employ it in some cases.For error analysis of the method,the residual of the solutions is reviewed.The reported examples show that the method is reasonably efficient and accurate. 展开更多
关键词 Coronavirus(COVID-19) SITR model exponential approximation differential equations system collocation method operational matrix
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BITS: an efficient transport solver based on a collocation method with B-spline basis
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作者 肖小涛 王少杰 +3 位作者 叶磊 戴宗良 潘成康 任启龙 《Plasma Science and Technology》 SCIE EI CAS CSCD 2023年第2期27-35,共9页
A B-spline Interpolation Transport Solver(BITS) based on a collocation method is developed. It solves transport equations as a generalized interpolation problem, taking the first-order accuracy in time and the second-... A B-spline Interpolation Transport Solver(BITS) based on a collocation method is developed. It solves transport equations as a generalized interpolation problem, taking the first-order accuracy in time and the second-order accuracy in space along with a predictor–corrector or under-relaxation iteration method. Numerical tests show that BITS can solve one-dimensional transport equations for tokamak plasma more accurately without additional computation cost, compared to the finite difference method transport solver which is widely used in existing tokamak transport codes. 展开更多
关键词 plasma simulation transport equation COLLOCATION B-SPLINE TOKAMAK
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Multiresolution method for bending of plates with complex shapes
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作者 Jizeng WANG Yonggu FENG +2 位作者 Cong XU Xiaojing LIU Youhe ZHOU 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI CSCD 2023年第4期561-582,共22页
A high-accuracy multiresolution method is proposed to solve mechanics problems subject to complex shapes or irregular domains.To realize this method,we design a new wavelet basis function,by which we construct a fifth... A high-accuracy multiresolution method is proposed to solve mechanics problems subject to complex shapes or irregular domains.To realize this method,we design a new wavelet basis function,by which we construct a fifth-order numerical scheme for the approximation of multi-dimensional functions and their multiple integrals defined in complex domains.In the solution of differential equations,various derivatives of the unknown function are denoted as new functions.Then,the integral relations between these functions are applied in terms of wavelet approximation of multiple integrals.Therefore,the original equation with derivatives of various orders can be converted to a system of algebraic equations with discrete nodal values of the highest-order derivative.During the application of the proposed method,boundary conditions can be automatically included in the integration operations,and relevant matrices can be assured to exhibit perfect sparse patterns.As examples,we consider several second-order mathematics problems defined on regular and irregular domains and the fourth-order bending problems of plates with various shapes.By comparing the solutions obtained by the proposed method with the exact solutions,the new multiresolution method is found to have a convergence rate of fifth order.The solution accuracy of this method with only a few hundreds of nodes can be much higher than that of the finite element method(FEM)with tens of thousands of elements.In addition,because the accuracy order for direct approximation of a function using the proposed basis function is also fifth order,we may conclude that the accuracy of the proposed method is almost independent of the equation order and domain complexity. 展开更多
关键词 MULTIRESOLUTION generalized Coiflet wavelet integral collocation method irregular domain complex shape high accuracy plate bending
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Stability of Three-Dimensional Interfacial Waves Under Subharmonic Disturbances
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作者 Nabil ALLALOU Mohammed DEBIANE Christian KHARIF 《China Ocean Engineering》 SCIE EI CSCD 2023年第4期558-567,共10页
This study examines the stability regimes of three-dimensional interfacial gravity waves.The numerical results of the linear stability analysis extend the three-dimensional surface waves results of Ioualalen and Khari... This study examines the stability regimes of three-dimensional interfacial gravity waves.The numerical results of the linear stability analysis extend the three-dimensional surface waves results of Ioualalen and Kharif(1994)to three-dimensional interfacial waves.An approach of the collocation type has been developed for this purpose.The equations of motion are reduced to an eigenvalue problem where the perturbations are spectrally decomposed into normal modes.The results obtained showed that the density ratio plays a stabilizing factor.In addition,the dominant instability is of three-dimensional structure,and it belongs to class I for all values of density ratio. 展开更多
关键词 short-crested interfacial waves linear stability collocation method Padéapproximant
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Korteweg-De Vries方程的Legendre时空谱配置方法
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作者 王川 乔炎 《Chinese Quarterly Journal of Mathematics》 2023年第4期392-400,共9页
A Legendre-Legendre spectral collocation scheme is constructed for Korteweg-de Vries(KdV)equation on bounded domain by using the Legendre collocation method in both time and space,which is a nonlinear matrix equation ... A Legendre-Legendre spectral collocation scheme is constructed for Korteweg-de Vries(KdV)equation on bounded domain by using the Legendre collocation method in both time and space,which is a nonlinear matrix equation that is changed to a nonlinear systems and can be solved by the usual fixed point iteration.Numerical results demonstrate the efficiency of the method and spectral accuracy. 展开更多
关键词 Korteweg-de Vries equation Space-time Legendre spectral collocation method Initial-boundary value problem
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A Comparative Study of the Usage of Synonyms Based on BNC-Taking Assessment and Evaluation as Examples
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作者 JIANG Tian-meng 《Journal of Literature and Art Studies》 2023年第1期29-35,共7页
The discrimination of synonyms has always been one of the great challenges for English learners.Taking assessment and evaluation as examples,this study analyses the similarities and differences of the two words,as wel... The discrimination of synonyms has always been one of the great challenges for English learners.Taking assessment and evaluation as examples,this study analyses the similarities and differences of the two words,as well as their usage from the perspectives of frequency,stylistics,collocation and semantic prosody with the help of British National Corpus,and demonstrates the importance of corpus retrieval tools in synonyms discrimination.Furthermore,this paper will give some suggestions for English learners and teachers in English vocabulary teaching. 展开更多
关键词 corpus linguistics SYNONYMS frequency STYLISTICS COLLOCATION semantic prosody
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