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HIGH ACCURACY FINITE VOLUME ELEMENT METHOD FOR TWO-POINT BOUNDARY VALUE PROBLEM OF SECOND ORDER ORDINARY DIFFERENTIAL EQUATIONS 被引量:4
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作者 Wang Tongke(王同科) 《Numerical Mathematics A Journal of Chinese Universities(English Series)》 SCIE 2002年第2期213-225,共13页
In this paper, a high accuracy finite volume element method is presented for two-point boundary value problem of second order ordinary differential equation, which differs from the high order generalized difference me... In this paper, a high accuracy finite volume element method is presented for two-point boundary value problem of second order ordinary differential equation, which differs from the high order generalized difference methods. It is proved that the method has optimal order error estimate O(h3) in H1 norm. Finally, two examples show that the method is effective. 展开更多
关键词 second order ordinary differential equation TWO-POINT boundary value problem high accuracy finite volume element method error estimate.
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Laguerre-Gauss collocation method for initial value problems of second order ODEs 被引量:1
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作者 严建平 郭本瑜 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2011年第12期1541-1564,共24页
This paper proposes a new collocation method for initial value problems of second order ODEs based on the Laguerre-Gauss interpolation. It provides the global numerical solutions and possesses the spectral accuracy. N... This paper proposes a new collocation method for initial value problems of second order ODEs based on the Laguerre-Gauss interpolation. It provides the global numerical solutions and possesses the spectral accuracy. Numerical results demonstrate its high efficiency. 展开更多
关键词 Laguerre-Gauss collocation method initial value problem second orderODEs
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Structure and Performance of Fe-N_x-C Catalyst for Oxygen Reduction Reaction Prepared by Vacuum Casting Method and the Second Pyrolysis 被引量:1
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作者 钱亚声 童磊 +2 位作者 邵宗贵 囤荣敏 李文木 《Chinese Journal of Structural Chemistry》 SCIE CAS CSCD 2018年第6期937-947,共11页
Affordable non-precious metal(NPM) catalysts played a vital role in the wide application of polymer electrolyte membrane fuel cells(PEMFC). In current work, a facile vacuum casting reacting method based on vacuum ... Affordable non-precious metal(NPM) catalysts played a vital role in the wide application of polymer electrolyte membrane fuel cells(PEMFC). In current work, a facile vacuum casting reacting method based on vacuum casting was introduced to prepare Fe-N_x-C oxygen reduction reaction(ORR) catalysts with high efficient in acid medium. The catalysts were prepared with ammonium ferrous sulfate hexahydrate(AFS) and 1,10-phenanthroline monohydrate utilizing homemade mesoporous silica template. The heat treatment and its influence on structure and performance were systematically evaluated to achieve superior ORR performance and some clues were found. And 850 ℃ was found to be the best temperature for the first and second pyrolysis. The linear sweep voltammetry(LSV) results showed that there were only 18 mV slightly negative shifts of half-wave potential(E_(1/2)) of the optimal catalyst(749 mV) compared with the commercial Pt/C(20 μg·Pt·cm^-2). Besides, I850 R also showed better electrochemical stability and methanol-tolerance than that of Pt/C. All evidences proved that our vacuum casting reacting strategy and heat treatment process were prospective for the future R&D of high performance Fe-N_x-C ORR catalysts. 展开更多
关键词 oxygen reduction reaction acid medium vacuum casting reacting method temperature affected structure second pyrolysis
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Two-grid partition of unity method for second order elliptic problems
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作者 王琤 黄自萍 李立康 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2008年第4期527-533,共7页
A two-grid partition of unity method for second order elliptic problems is proposed and analyzed. The standard two-grid method is a local and parallel method usually leading to a discontinuous solution in the entire c... A two-grid partition of unity method for second order elliptic problems is proposed and analyzed. The standard two-grid method is a local and parallel method usually leading to a discontinuous solution in the entire computational domain. Partition of unity method is employed to glue all the local solutions together to get the global continuous one, which is optimal in HI-norm. Furthermore, it is shown that the L^2 error can be improved by using the coarse grid correction. Numerical experiments are reported to support the theoretical results. 展开更多
关键词 second order elliptic problems two-grid method partition of unity
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AN ADI GALERKIN METHOD WITH MOVING FINITE ELEMENT SPACES FOR A CLASS OF SECOND-ORDER HYPERBOLIC EQUATIONS
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作者 孙同军 《Numerical Mathematics A Journal of Chinese Universities(English Series)》 SCIE 2001年第1期45-58,共14页
An alternating direction implicit (ADI) Galerkin method with moving finite element spaces is formulated for a class of second order hyperbolic equations in two space variables. A priori H 1 error estimate is derived.
关键词 alternating direction implicit method moving finite element second order hyperbolic equations.
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A Semi-Analytical Method for Solutions of a Certain Class of Second Order Ordinary Differential Equations
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作者 S. O. Edeki H. I. Okagbue +1 位作者 A. A. Opanuga S. A. Adeosun 《Applied Mathematics》 2014年第13期2034-2041,共8页
This paper presents the theory and applications of a new computational technique referred to as Differential Transform Method (DTM) for solving second order linear ordinary differential equations, for both homogeneous... This paper presents the theory and applications of a new computational technique referred to as Differential Transform Method (DTM) for solving second order linear ordinary differential equations, for both homogeneous and nonhomogeneous cases. For the robustness and efficiency of the method, four examples are considered. The results indicate that the DTM is reliable and accurate when compared to the exact solutions of the solved problems. 展开更多
关键词 Differential TRANSFORM method second Order ODES Linear Systems Series Solution
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The Successive Approximation Method for Solving Nonlinear Fredholm Integral Equation of the Second Kind Using Maple
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作者 Dalal Adnan Maturi 《Advances in Pure Mathematics》 2019年第10期832-843,共12页
In this paper, we will use the successive approximation method for solving Fredholm integral equation of the second kind using Maple18. By means of this method, an algorithm is successfully established for solving the... In this paper, we will use the successive approximation method for solving Fredholm integral equation of the second kind using Maple18. By means of this method, an algorithm is successfully established for solving the non-linear Fredholm integral equation of the second kind. Finally, several examples are presented to illustrate the application of the algorithm and results appear that this method is very effective and convenient to solve these equations. 展开更多
关键词 NONLINEAR FREDHOLM INTEGRAL Equation of the second KIND Successive Approximation method Maple18
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Explicit Iterative Methods of Second Order and Approximate Inverse Preconditioners for Solving Complex Computational Problems
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作者 Anastasia-Dimitra Lipitakis 《Applied Mathematics》 2020年第4期307-327,共21页
Explicit Exact and Approximate Inverse Preconditioners for solving complex linear systems are introduced. A class of general iterative methods of second order is presented and the selection of iterative parameters is ... Explicit Exact and Approximate Inverse Preconditioners for solving complex linear systems are introduced. A class of general iterative methods of second order is presented and the selection of iterative parameters is discussed. The second order iterative methods behave quite similar to first order methods and the development of efficient preconditioners for solving the original linear system is a decisive factor for making the second order iterative methods superior to the first order iterative methods. Adaptive preconditioned Conjugate Gradient methods using explicit approximate preconditioners for solving efficiently large sparse systems of algebraic equations are also presented. The generalized Approximate Inverse Matrix techniques can be efficiently used in conjunction with explicit iterative schemes leading to effective composite semi-direct solution methods for solving large linear systems of algebraic equations. 展开更多
关键词 APPROXIMATE INVERSE PRECONDITIONERS ITERATIVE methodS second Order ITERATIVE Schemes Exact INVERSE methodS APPROXIMATE INVERSE EXPLICIT Preconditioning Conjugate Gradients Convergence Analysis
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A Second Order Characteristic Mixed Finite Element Method for Convection Diffusion Reaction Equations
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作者 Tongjun Sun 《Journal of Applied Mathematics and Physics》 2017年第6期1301-1319,共19页
A combined approximate scheme is defined for convection-diffusion-reaction equations. This scheme is constructed by two methods. Standard mixed finite element method is used for diffusion term. A second order characte... A combined approximate scheme is defined for convection-diffusion-reaction equations. This scheme is constructed by two methods. Standard mixed finite element method is used for diffusion term. A second order characteristic finite element method is presented to handle the material derivative term, that is, the time derivative term plus the convection term. The stability is proved and the L2-norm error estimates are derived for both the scalar unknown variable and its flux. The scheme is of second order accuracy in time increment, symmetric, and unconditionally stable. 展开更多
关键词 Mixed Finite Element method CHARACTERISTIC method second Order Accuracy CONVECTION Diffusion REACTION EQUATIONS
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Differential Quadrature Method for Steady Flow of an Incompressible Second-Order Viscoelastic Fluid and Heat Transfer Model 被引量:1
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作者 A.S.J.AL-SAIF 朱正佑 《Journal of Shanghai University(English Edition)》 CAS 2005年第4期298-305,共8页
The two-dimensional steady flow of an incompressible second-order viscoelastic fluid between two parallel plates was studied in terms of vorticity, the stream function and temperature equations. The governing equation... The two-dimensional steady flow of an incompressible second-order viscoelastic fluid between two parallel plates was studied in terms of vorticity, the stream function and temperature equations. The governing equations were expanded with respect to a snmll parameter to get the zeroth- and first-order approximate equations. By using the differenl2al quadrature method with only a few grid points, the high-accurate numerical results were obtained. 展开更多
关键词 differential quadrature method(DQM) second-order viscoelastic fluid steady flow heat transfer.
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Research on the Related Factors of the Second Molar Dislocation and Orthodontic Erect Method
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作者 Jinhong Guo 《Journal of Advances in Medicine Science》 2020年第1期44-47,共4页
The second molar dislocation is more common clinically.To investigate the related factors of the second permanent molar dislocation,and provide reference for the clinical diagnosis and treatment of orthodontics.From t... The second molar dislocation is more common clinically.To investigate the related factors of the second permanent molar dislocation,and provide reference for the clinical diagnosis and treatment of orthodontics.From the current clinical research,the clinical methods of orthodontic erect secondary molars are also diverse and clinical.The narrower first molar alveolar arch width,smaller ANB angle,and crowded maxillary posterior segment arch are the factors that cause the maxillary second permanent molar dislocation.The narrow alveolar arch width,the smaller SNB angle,the larger ANB angle,and the crowded lower mandibular arch are the factors leading to the dislocation of the mandibular second permanent molar.In addition,for the second mandibular molar malposition,it is particularly important to select the corrective treatment plan.It is especially important to improve the treatment. 展开更多
关键词 MANDIBULAR second MOLAR MALPOSITION Etiology ORTHODONTIC erect Classification diagnosis Best method
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Application of diflerential constraint method to exact solution of second-grade fluid
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作者 张道祥 冯素晓 +1 位作者 卢志明 刘宇陆 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2009年第4期403-412,共10页
A differential constraint method is used to obtain analytical solutions of a second-grade fluid flow. By using the first-order differential constraint condition, exact solutions of Poiseuille flows, jet flows and Coue... A differential constraint method is used to obtain analytical solutions of a second-grade fluid flow. By using the first-order differential constraint condition, exact solutions of Poiseuille flows, jet flows and Couette flows subjected to suction or blowing forces, and planar elongational flows are derived. In addition, two new classes of exact solutions for a second-grade fluid flow are found. The obtained exact solutions show that the non-Newtonian second-grade flow behavior depends not only on the material viscosity but also on the material elasticity. Finally, some boundary value problems are discussed. 展开更多
关键词 non-Newtonian fluid differential constraint method second-grade fluid
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Second-order two-scale computational method for ageing linear viscoelastic problem in composite materials with periodic structure
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作者 Yang ZHANG Junzhi CUI Yufeng NIE 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI CSCD 2016年第2期253-264,共12页
The correspondence principle is an important mathematical technique to compute the non-ageing linear viscoelastic problem as it allows to take advantage of the computational methods originally developed for the elasti... The correspondence principle is an important mathematical technique to compute the non-ageing linear viscoelastic problem as it allows to take advantage of the computational methods originally developed for the elastic case. However, the correspon- dence principle becomes invalid when the materials exhibit ageing. To deal with this problem, a second-order two-scale (SOTS) computational method in the time domain is presented to predict the ageing linear viscoelastic performance of composite materials with a periodic structure. First, in the time domain, the SOTS formulation for calcu- lating the effective relaxation modulus and displacement approximate solutions of the ageing viscoelastic problem is formally derived. Error estimates of the displacement ap- proximate solutions for SOTS method are then given. Numerical results obtained by the SOTS method are shown and compared with those by the finite element method in a very fine mesh. Both the analytical and numerical results show that the SOTS computational method is feasible and efficient to predict the ageing linear viscoelastic performance of composite materials with a periodic structure. 展开更多
关键词 second-order two-scale (SOTS) method ageing VISCOELASTICITY composite material periodic structure
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Interaction solutions for the second extended(3+1)-dimensional Jimbo–Miwa equation
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作者 马红彩 毛雪 邓爱平 《Chinese Physics B》 SCIE EI CAS CSCD 2023年第6期112-121,共10页
Based on the Hirota bilinear method,the second extended(3+1)-dimensional Jimbo–Miwa equation is established.By Maple symbolic calculation,lump and lump-kink soliton solutions are obtained.The interaction solutions be... Based on the Hirota bilinear method,the second extended(3+1)-dimensional Jimbo–Miwa equation is established.By Maple symbolic calculation,lump and lump-kink soliton solutions are obtained.The interaction solutions between the lump and multi-kink soliton,and the interaction between the lump and triangular periodic soliton are derived by combining a multi-exponential function or trigonometric sine and cosine functions with quadratic functions.Furthermore,periodiclump wave solution is derived via the ansatz including hyperbolic and trigonometric functions.Finally,3D plots,2D curves,density plots,and contour plots with particular choices of the suitable parameters are depicted to illustrate the dynamical features of these solutions. 展开更多
关键词 Hirota bilinear method second extended(3+1)-dimensional Jimbo–Miwa equation lump solution interaction solution
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P-and S-wavefield simulations using both the firstand second-order separated wave equations through a high-order staggered grid finite-difference method
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作者 Chao-ying Bai Xin Wang Cai-xia Wang 《Earthquake Science》 2013年第2期83-98,共16页
In seismic exploration, it is common practice to separate the P-wavefield from the S-wavefield by the elastic wavefield decomposition technique, for imaging purposes. However, it is sometimes difficult to achieve this... In seismic exploration, it is common practice to separate the P-wavefield from the S-wavefield by the elastic wavefield decomposition technique, for imaging purposes. However, it is sometimes difficult to achieve this, especially when the velocity field is complex. A useful approach in multi-component analysis and modeling is to directly solve the elastic wave equations for the pure P- or S-wavefields, referred as the separate elastic wave equa- tions. In this study, we compare two kinds of such wave equations: the first-order (velocity-stress) and the second- order (displacement-stress) separate elastic wave equa- tions, with the first-order (velocity-stress) and the second- order (displacement-stress) full (or mixed) elastic wave equations using a high-order staggered grid finite-differ- ence method. Comparisons are given of wavefield snap- shots, common-source gather seismic sections, and individual synthetic seismogram. The simulation tests show that equivalent results can be obtained, regardless of whether the first-order or second-order separate elastic wave equations are used for obtaining the pure P- or S-wavefield. The stacked pure P- and S-wavefields are equal to the mixed wave fields calculated using the corre- sponding first-order or second-order full elastic wave equations. These mixed equations are computationallyslightly less expensive than solving the separate equations. The attraction of the separate equations is that they achieve separated P- and S-wavefields which can be used to test the efficacy of wave decomposition procedures in multi-com- ponent processing. The second-order separate elastic wave equations are a good choice because they offer information on the pure P-wave or S-wave displacements. 展开更多
关键词 Finite-difference method Staggeredgrid First-order separate elastic wave equation second-order separate elastic wave equation Multiple arrival tracking
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一个解特定二阶驻定方程的新方法——特征伴随方程法
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作者 韩松 张明俊 何晓莹 《广西科技大学学报》 CAS 2024年第1期131-138,共8页
本文对文献[1]中提出的一类二阶驻定方程G″/G=∑^(m)_(j=0)P_(j)(G′/G)^(j)的求法进行探讨,提出了全新的求解方法——特征伴随方程法,通过该求法得到这类方程当m取不同非负整数(本文仅讨论m=2)时的通解,并相应给出该方程作为求解非线... 本文对文献[1]中提出的一类二阶驻定方程G″/G=∑^(m)_(j=0)P_(j)(G′/G)^(j)的求法进行探讨,提出了全新的求解方法——特征伴随方程法,通过该求法得到这类方程当m取不同非负整数(本文仅讨论m=2)时的通解,并相应给出该方程作为求解非线性偏微分方程的辅助方程时所需要的G′/G的解析表达式;同时给出一个作为常微分方程中驻定方程的应用实例,以及该方程作为非线性偏微分方程的辅助方程时利用扩展G′/G展开法的求解例子,通过该实例给出方程的精确行波解。 展开更多
关键词 二阶驻定方程 特征方程 指数变换 特征伴随方程(法) 降阶法 异型通解
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极限下限分析的区域光滑径向点插值法
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作者 陈莘莘 董昊 李庆华 《力学季刊》 CAS CSCD 北大核心 2024年第3期697-705,共9页
极限分析的高效数值计算方法在结构设计和安全评定中具有非常重要的作用.为了更加有效地求解极限分析问题,将区域光滑径向点插值法与二阶锥规划相结合,提出了理想弹塑性结构极限下限分析的一种新方法.将问题域离散为简单的三角形背景单... 极限分析的高效数值计算方法在结构设计和安全评定中具有非常重要的作用.为了更加有效地求解极限分析问题,将区域光滑径向点插值法与二阶锥规划相结合,提出了理想弹塑性结构极限下限分析的一种新方法.将问题域离散为简单的三角形背景单元,每个单元进一步划分成若干个光滑域.为了将复杂的域积分转化为简单的边界积分,并且避免计算形函数的导数,采用广义梯度光滑技术对每个光滑域进行应变光滑处理.由于径向点插值法构造的形函数满足Kronecker delta性质,本质边界条件可以直接施加.依据下限定理,在满足以等效积分弱形式表达的自平衡应力场平衡条件的基础上,用二阶锥规划成功构建了极限分析下限法的计算模型,从而可方便地通过基于原始-对偶内点法的数学规划求解器MOSEK直接求解该问题.数值算例结果表明,本文所提方法有效地克服了维数障碍问题,具有较高的计算精度,并且计算结果对网格畸变十分不敏感. 展开更多
关键词 无网格法 区域光滑径向点插值法 极限下限分析 广义梯度光滑技术 二阶锥规划
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基于日语特点的“应用型”二外日语教学、考核方式探索与实践
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作者 彭贞 胡永近 《宿州学院学报》 2024年第5期76-80,共5页
针对目前应用型本科高校中日语教学质量普遍不高、课堂气氛低迷、学生学习热情不高的现象,通过对日语特点的分析,提出了基于日语特点的“导”“借”“设”“比”四个层次的日语教学方式。在上述教学方式的实施过程中,提出了适应上述教... 针对目前应用型本科高校中日语教学质量普遍不高、课堂气氛低迷、学生学习热情不高的现象,通过对日语特点的分析,提出了基于日语特点的“导”“借”“设”“比”四个层次的日语教学方式。在上述教学方式的实施过程中,提出了适应上述教学方式的全程基础性考核、学生“应用型”表现实时考核、客观公正的多方性考核相结合的“应用型”日语考核方式,并对该考核方式对应的指标进行了量化细分,以便于应用;将上述考核方式应用于教学过程,并对考核结果进行了分析,发现考核分数分布合理、区分度较好。 展开更多
关键词 日语特点 二外 应用型 教学方式 考核方式
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含电动汽车的主动配电网多目标分层优化调度
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作者 杨晓辉 王晓鹏 邓叶恒 《电力工程技术》 北大核心 2024年第4期156-165,共10页
为了协调电动汽车车主和主动配电网2个不同主体之间的利益关系,针对电动汽车接入后主动配电网的优化调度问题,文中提出一种考虑电动汽车充电综合满意度和主动配电网运行效益的多目标分层优化方法。上层模型注重最大化电动汽车车主的充... 为了协调电动汽车车主和主动配电网2个不同主体之间的利益关系,针对电动汽车接入后主动配电网的优化调度问题,文中提出一种考虑电动汽车充电综合满意度和主动配电网运行效益的多目标分层优化方法。上层模型注重最大化电动汽车车主的充电利益,采用归一化法向约束法求解电动汽车的最优充放电计划,并将其输入下层优化模型。下层模型旨在最大化主动配电网的运行效益,根据电动汽车的充放电计划调整可控分布式电源的输出功率,采用二阶锥松弛转换法和带权极小模理想点法求解该非线性多目标问题。仿真结果表明,所提含电动汽车的主动配电网多目标分层优化方法能够在促使电动汽车充电综合满意度超过0.9的同时,减少有功网损约94.12%、运行成本约30.90%,实现电动汽车车主和主动配电网的双赢。 展开更多
关键词 电动汽车 主动配电网 分层优化 多目标优化 归一化法向约束法 带权极小模理想点法 二阶锥松弛转化法
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基于二次指数平滑和多元线性回归的宁波市港口物流需求预测分析
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作者 张志清 杜静 《物流科技》 2024年第17期78-82,共5页
随着经济全球化的发展,港口作为物流发展的重要环节,港口物流需求已经成为港口资源配置规划和进出口贸易的重要依据。为对宁波市港口物流需求进行科学合理的预测,文章借助SPSS等数据分析软件,使用二次指数平滑和多元线性回归分别对其物... 随着经济全球化的发展,港口作为物流发展的重要环节,港口物流需求已经成为港口资源配置规划和进出口贸易的重要依据。为对宁波市港口物流需求进行科学合理的预测,文章借助SPSS等数据分析软件,使用二次指数平滑和多元线性回归分别对其物流需求进行预测,通过对比两种预测方法的精度,最后发现,二次指数平滑法的预测精确度要优于多元线性回归法,并通过二次指数平滑法预测宁波市未来五年的港口物流需求量。 展开更多
关键词 二次指数平滑 多元线性回归 港口物流需求预测
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