期刊文献+
共找到48篇文章
< 1 2 3 >
每页显示 20 50 100
ON A REGULARIZATION OF INDEX 2 DIFFERENTIAL-ALGEBRAIC EQUATIONS WITH PROPERLY STATED LEADING TERM
1
作者 刘红 宋永忠 《Acta Mathematica Scientia》 SCIE CSCD 2011年第2期383-398,共16页
In this article, linear regular index 2 DAEs A(t)[D(t)x(t)]' + B(t)x(t) = q(t) are considered. Using a decoupling technique, initial condition and boundary condition are properly formulated. Regular inde... In this article, linear regular index 2 DAEs A(t)[D(t)x(t)]' + B(t)x(t) = q(t) are considered. Using a decoupling technique, initial condition and boundary condition are properly formulated. Regular index 1 DAEs are obtained by a regularization method. We study the behavior of the solution of the regularization system via asymptotic expansions. The error analysis between the solutions of the DAEs and its regularization system is given. 展开更多
关键词 differential-algebraic equations (daes properly stated leading term in-dex REGULARIZATION
下载PDF
SOlvaBILITY OF HIGHER INDEX TIME-VARYING LINEAR DIFFERENTIAL-ALGEBRAIC EQUATIONS 被引量:1
2
作者 宋永忠 《Acta Mathematica Scientia》 SCIE CSCD 2001年第1期77-92,共16页
Linear differential-algebraic equations (DAEs) with time-varying coefficients A(t)x(1)(t) + B(t)x(t) = q(t), which are tractable with a higher index. are discussed. Their essential properties are investigated. Some eq... Linear differential-algebraic equations (DAEs) with time-varying coefficients A(t)x(1)(t) + B(t)x(t) = q(t), which are tractable with a higher index. are discussed. Their essential properties are investigated. Some equivalent system,,; are given. Using them the paper shows how to state properly initial and boundary conditions for these DAEs. The existence and uniqueness theory of the solution of the initial and boundary value problems for higher index DAEs are proposed. 展开更多
关键词 differential-algebraic equations INDEX SOLVABILITY EXISTENCE UNIQUENESS
下载PDF
NONNEGATIVITY OF SOLUTIONS OF NONLINEAR FRACTIONAL DIFFERENTIAL-ALGEBRAIC EQUATIONS
3
作者 Xiaoli DING Yaolin JIANG 《Acta Mathematica Scientia》 SCIE CSCD 2018年第3期756-768,共13页
Nonlinear fractional differential-algebraic equations often arise in simulating integrated circuits with superconductors. How to obtain the nonnegative solutions of the equations is an important scientific problem. As... Nonlinear fractional differential-algebraic equations often arise in simulating integrated circuits with superconductors. How to obtain the nonnegative solutions of the equations is an important scientific problem. As far as we known, the nonnegativity of solutions of the nonlinear fractional differential-algebraic equations is still not studied. In this article, we investigate the nonnegativity of solutions of the equations. Firstly, we discuss the existence of nonnegative solutions of the equations, and then we show that the nonnegative solution can be approached by a monotone waveform relaxation sequence provided the initial iteration is chosen properly. The choice of initial iteration is critical and we give a method of finding it. Finally, we present an example to illustrate the efficiency of our method. 展开更多
关键词 Fractional differential-algebraic equations nonnegativity of solutions waveform relaxation monotone convergence
下载PDF
Efficient Numerical Methods for Solving Differential Algebraic Equations 被引量:2
4
作者 Ampon Dhamacharoen 《Journal of Applied Mathematics and Physics》 2016年第1期39-47,共9页
This research aims to solve Differential Algebraic Equation (DAE) problems in their original form, wherein both the differential and algebraic equations remain. The Newton or Newton-Broyden technique along with some i... This research aims to solve Differential Algebraic Equation (DAE) problems in their original form, wherein both the differential and algebraic equations remain. The Newton or Newton-Broyden technique along with some integrators such as the Runge-Kutta method is coupled together to solve the problems. Experiments show that the method developed in this paper is efficient, as it demonstrates that implementation of the method is not difficult, and such method is able to provide approximate solutions with ease within some desired accuracy standards. 展开更多
关键词 differential-algebraic equations Newton-Broyden Method Index-2 Hessenberg dae
下载PDF
Numerical Integration for DAEs of Multibody System Dynamics
5
作者 GENG Guo-zhi LIU Jian-wen DING Jie-yu 《科技视界》 2015年第15期12-13,24,共3页
During the simulation of constrained multibody system,numerical integration is important for solving the Euler-Lagrange equation of multibody system dynamics,which is usually a Differential-Algebraic Equations(DAEs).U... During the simulation of constrained multibody system,numerical integration is important for solving the Euler-Lagrange equation of multibody system dynamics,which is usually a Differential-Algebraic Equations(DAEs).Using the discrete Hamilton principle,discrete EulerLagrangian equation is obtained first based on Lagrange Interpolation.Then the Romberg,Gauss integral is used to solve the DAEs.At last,numerical results are compared by using Euler method,Runge-Kutta method,Romberg method and Gauss method for a double pendulum system. 展开更多
关键词 数值积分 多体系动力学 科学研究 微分代数
下载PDF
A multiscale differential-algebraic neural network-based method for learning dynamical systems
6
作者 Yin Huang Jieyu Ding 《International Journal of Mechanical System Dynamics》 EI 2024年第1期77-87,共11页
The objective of dynamical system learning tasks is to forecast the future behavior of a system by leveraging observed data.However,such systems can sometimes exhibit rigidity due to significant variations in componen... The objective of dynamical system learning tasks is to forecast the future behavior of a system by leveraging observed data.However,such systems can sometimes exhibit rigidity due to significant variations in component parameters or the presence of slow and fast variables,leading to challenges in learning.To overcome this limitation,we propose a multiscale differential-algebraic neural network(MDANN)method that utilizes Lagrangian mechanics and incorporates multiscale information for dynamical system learning.The MDANN method consists of two main components:the Lagrangian mechanics module and the multiscale module.The Lagrangian mechanics module embeds the system in Cartesian coordinates,adopts a differential-algebraic equation format,and uses Lagrange multipliers to impose constraints explicitly,simplifying the learning problem.The multiscale module converts high-frequency components into low-frequency components using radial scaling to learn subprocesses with large differences in velocity.Experimental results demonstrate that the proposed MDANN method effectively improves the learning of dynamical systems under rigid conditions. 展开更多
关键词 dynamical systems learning multibody system dynamics differential-algebraic equation neural networks multiscale structures
原文传递
PDE与DAE耦合系统求解方法
7
作者 李志华 杨红光 喻军 《计算机辅助设计与图形学学报》 EI CSCD 北大核心 2014年第1期106-112,共7页
针对目前Modelica语言只能解决由微分代数方程(DAE)描述的问题,而不能解决由偏微分方程(PDE)表达的问题,提出一种求解PDE与DAE耦合系统的方法.首先采用径向基函数构造近似函数,将未知量场函数的时空变量分开;然后运用配点法对空间变量... 针对目前Modelica语言只能解决由微分代数方程(DAE)描述的问题,而不能解决由偏微分方程(PDE)表达的问题,提出一种求解PDE与DAE耦合系统的方法.首先采用径向基函数构造近似函数,将未知量场函数的时空变量分开;然后运用配点法对空间变量进行离散,从而将PDE问题转化为DAE问题;最后采用成熟的DAE求解器进行求解,得到场函数在任意时空点的函数值.实例结果表明,该方法在不改变Modelica语法的前提下,能较好地实现PDE与DAE耦合系统的一致求解,且求解精度高、稳定性好、边界条件处理简单. 展开更多
关键词 多领域统一建模 MODELICA 偏微分方程 微分代数方程 耦合系统
下载PDF
A GENERAL CLASS OF ONE-STEP APPROXIMATION FOR INDEX-1 STOCHASTIC DELAY-DIFFERENTIAL-ALGEBRAIC *EQUATIONS 被引量:1
8
作者 Tingting Qin Chengjian Zhang 《Journal of Computational Mathematics》 SCIE CSCD 2019年第2期151-169,共19页
This paper develops a class of general one-step discretization methods for solving the index-1 stochastic delay differential-algebraic equations. The existence and uniqueness theorem of strong solutions of index-1 equ... This paper develops a class of general one-step discretization methods for solving the index-1 stochastic delay differential-algebraic equations. The existence and uniqueness theorem of strong solutions of index-1 equations is given. A strong convergence criterion of the methods is derived, which is applicable to a series of one-step stochastic numerical methods. Some specific numerical methods, such as the Euler-Maruyama method, stochastic ^-methods, split-step ^-methods are proposed, and their strong convergence results are given. Numerical experiments further illustrate the theoretical results. 展开更多
关键词 Stochastic delay differential-algebraic equations ONE-STEP DISCRETIZATION schemes Strong convergence
原文传递
Convergence of Linear Multistep Methods and One-Leg Methods for Index-2 Differential-Algebraic Equations with a Variable Delay 被引量:2
9
作者 Hongliang Liu Aiguo Xiao 《Advances in Applied Mathematics and Mechanics》 SCIE 2012年第5期636-646,共11页
Linear multistep methods and one-leg methods are applied to a class of index-2 nonlinear differential-algebraic equations with a variable delay.The corresponding convergence results are obtained and successfully confi... Linear multistep methods and one-leg methods are applied to a class of index-2 nonlinear differential-algebraic equations with a variable delay.The corresponding convergence results are obtained and successfully confirmed by some numerical examples.The results obtained in this work extend the corresponding ones in literature. 展开更多
关键词 index-2 differential-algebraic equations variable delay linear mutistep methods one-leg methods CONVERGENCE
原文传递
Legendre Neural Network for Solving Linear Variable Coefficients Delay Differential-Algebraic Equations with Weak Discontinuities 被引量:2
10
作者 Hongliang Liu Jingwen Song +2 位作者 Huini Liu Jie Xu Lijuan Li 《Advances in Applied Mathematics and Mechanics》 SCIE 2021年第1期101-118,共18页
In this paper,we propose a novel Legendre neural network combined with the extreme learning machine algorithm to solve variable coefficients linear delay differential-algebraic equations with weak discontinuities.Firs... In this paper,we propose a novel Legendre neural network combined with the extreme learning machine algorithm to solve variable coefficients linear delay differential-algebraic equations with weak discontinuities.First,the solution interval is divided into multiple subintervals by weak discontinuity points.Then,Legendre neural network is used to eliminate the hidden layer by expanding the input pattern using Legendre polynomials on each subinterval.Finally,the parameters of the neural network are obtained by training with the extreme learning machine.The numerical examples show that the proposed method can effectively deal with the difficulty of numerical simulation caused by the discontinuities. 展开更多
关键词 CONVERGENCE delay differential-algebraic equations Legendre activation function neural network.
原文传递
ON SOLVABILITY AND WAVEFORM RELAXATION METHODS FOR LINEAR VARIABLE-COEFFICIENT DIFFERENTIAL-ALGEBRAIC EQUATIONS
11
作者 Xi Yang 《Journal of Computational Mathematics》 SCIE CSCD 2014年第6期696-720,共25页
This paper is concerned with the solvability and waveform relaxation methods of linear variable-coefficient differential-algebraic equations (DAEs). Most of the previous works have been focused on linear variable-co... This paper is concerned with the solvability and waveform relaxation methods of linear variable-coefficient differential-algebraic equations (DAEs). Most of the previous works have been focused on linear variable-coefficient DAEs with smooth coefficients and data, yet no results related to the convergence rate of the corresponding waveform relaxation methods has been obtained. In this paper, we develope the solvability theory for the linear variable-coefficient DAEs on Legesgue square-integrable function space in both traditional and least squares senses, and determine the convergence rate of the waveform relaxation methods for solving linear variable-coefficient DAEs. 展开更多
关键词 differential-algebraic equations Integral operator Fourier transform Wave-form relaxation method.
原文传递
LYAPUNOV-LIKE EXPONENTIAL STABILITY AND UNSTABILITY OF DIFFERENTIAL-ALGEBRAIC EQUATION 被引量:1
12
作者 温香彩 丘水生 郭清溥 《Annals of Differential Equations》 1997年第2期170-179,共10页
In this paper, Lyapunov-like exponential stability and unstability of differentialalgebraic equation are considered from the viewpoint of stability of system motion, and the criteria of exponential stability and unsta... In this paper, Lyapunov-like exponential stability and unstability of differentialalgebraic equation are considered from the viewpoint of stability of system motion, and the criteria of exponential stability and unstability of nonlinear nonautonomous differential-algebraic equation are given by using Lyapunov-like function similar to ordinary differential equation. 展开更多
关键词 differential-algebraic equation exponential stability g-solution K class function
原文传递
Three Dimensional Electric Circuits with Multiple Capacitors and Resistors
13
作者 Haiduke Sarafian 《American Journal of Computational Mathematics》 2023年第3期379-386,共8页
Two cubical 3D electric circuits with single and double capacitors and twelve ohmic resistors are considered. The resistors are the sides of the cube. The circuit is fed with a single internal emf. The charge on the c... Two cubical 3D electric circuits with single and double capacitors and twelve ohmic resistors are considered. The resistors are the sides of the cube. The circuit is fed with a single internal emf. The charge on the capacitor(s) and the current distributions of all twelve sides of the circuit(s) vs. time are evaluated. The analysis requires solving twelve differential-algebraic intertwined symbolic equations. This is accomplished by applying a Computer Algebra System (CAS), specifically Mathematica. The needed codes are included. For a set of values assigned to the elements, the numeric results are depicted. 展开更多
关键词 3D Electric Circuits Capacitors Multiple Resistors differential-algebraic equations Computer Algebra System MATHEMATICA
下载PDF
一种基于投影积分算法的微电网稳定性仿真方法 被引量:6
14
作者 李鹏 原凯 +2 位作者 王成山 黄小耘 黄红远 《电工技术学报》 EI CSCD 北大核心 2014年第2期93-101,共9页
微电网中形式各异的分布式电源使其在动态响应上体现为多时间尺度特征,其稳定性仿真算法在数值稳定性和计算效率方面需要满足更高的要求。本文提出一种基于投影积分算法的微电网稳定性仿真方法,每一个投影积分步由若干小步长积分步(内... 微电网中形式各异的分布式电源使其在动态响应上体现为多时间尺度特征,其稳定性仿真算法在数值稳定性和计算效率方面需要满足更高的要求。本文提出一种基于投影积分算法的微电网稳定性仿真方法,每一个投影积分步由若干小步长积分步(内部积分器)和一个大步长积分步(外部积分器)组成,仿真步长及投影步长可根据系统快、慢动态响应的时间常数选取,可有效实现传统显式积分算法数值稳定性的提升,且为2阶精度算法。以一个低压微电网为例,通过与商业仿真软件的仿真结果进行比较,验证了算法的正确性和有效性。 展开更多
关键词 微电网 稳定性仿真 投影积分算法 微分-代数方程 MICROGRID (MG) differential-algebraic equatION (dae)
下载PDF
电力市场稳定性分析 被引量:19
15
作者 杨志辉 刘有非 +1 位作者 唐云 吴复立 《中国电机工程学报》 EI CSCD 北大核心 2005年第2期1-5,共5页
电力市场利用市场机制的手段合理分配电力系统资源,其稳定性研究对于调节市场供需状况具有十分重要的意义。针对一类考虑阻塞条件的动态电力市场模型,该文给出了一系列充分条件来判断电力市场的稳定性。通过这些充分条件,电力市场的... 电力市场利用市场机制的手段合理分配电力系统资源,其稳定性研究对于调节市场供需状况具有十分重要的意义。针对一类考虑阻塞条件的动态电力市场模型,该文给出了一系列充分条件来判断电力市场的稳定性。通过这些充分条件,电力市场的稳定性可以不通过计算或较少的符号计算得到,这使得判断电力市场稳定性更加方便且准确。此外,利用该文的理论结果还可以合理解释由Alvarado提出的电力市场不稳定模型,并且这些结果还为控制电力市场稳定性提供理论依据。 展开更多
关键词 电力系统 稳定性分析 电力市场 动力学 动态市场模型
下载PDF
非线性微分-代数系统的输出反馈镇定控制 被引量:7
16
作者 臧强 戴先中 《自动化学报》 EI CSCD 北大核心 2009年第9期1244-1248,共5页
对满足线性增长条件的非线性微分-代数系统,研究了其输出反馈镇定控制问题.通过将状态观测器与控制器耦合在一起设计,构造出一种非初始化的线性高增益状态观测器,具有良好的鲁棒性.基于反推设计方法构造出一个线性的动态输出补偿器,使... 对满足线性增长条件的非线性微分-代数系统,研究了其输出反馈镇定控制问题.通过将状态观测器与控制器耦合在一起设计,构造出一种非初始化的线性高增益状态观测器,具有良好的鲁棒性.基于反推设计方法构造出一个线性的动态输出补偿器,使得整个闭环系统是渐近稳定的.仿真结果验证了本文所提控制方法的有效性. 展开更多
关键词 微分-代数系统 非线性系统 输出反馈 渐近镇定 反推
下载PDF
基于θ_1方法的多体动力学数值算法研究 被引量:5
17
作者 马秀腾 翟彦博 罗书强 《力学学报》 EI CSCD 北大核心 2011年第5期931-938,共8页
将结构动力学领域的θ_1方法拓展到数值求解多体系统运动方程——微分-代数方程(DAEs),分别求解指标-3 DAEs形式的运动方程和指标-2超定DAEs(ODAEs)形式的运动方程.通过数值算例验证了方法的有效性,并得到θ_1方法中参数θ_1的选取与数... 将结构动力学领域的θ_1方法拓展到数值求解多体系统运动方程——微分-代数方程(DAEs),分别求解指标-3 DAEs形式的运动方程和指标-2超定DAEs(ODAEs)形式的运动方程.通过数值算例验证了方法的有效性,并得到θ_1方法中参数θ_1的选取与数值耗散量之间的关系.数值算例还说明对于同一个多体系统,采用指标-3的DAEs描述时存在速度违约,用指标-2的ODAEs描述时,从计算机精度上讲,位置和速度约束方程同时满足,并且θ_1方法在求解非保守系统DAEs和ODAEs形式的运动方程时都具有2阶精度.最后θ_1方法与其他直接积分法求解DAEs和ODAEs形式运动方程的CPU时间进行了比较. 展开更多
关键词 θ1-方法 多体系统 微分-代数方程(daes) 数值耗散 2阶精度
下载PDF
偏微分方程与微分代数方程的一致求解方法 被引量:3
18
作者 李志华 喻军 杨红光 《中国机械工程》 EI CAS CSCD 北大核心 2015年第4期441-445,共5页
Modelica语言是一种复杂物理系统多领域统一建模语言,但目前该语言只能解决由微分代数方程(DAE)描述的问题,而不能解决由偏微分方程(PDE)表达的问题。为此,提出一种偏微分方程与微分代数方程的一致求解方法,利用所构建的径向基函数配点... Modelica语言是一种复杂物理系统多领域统一建模语言,但目前该语言只能解决由微分代数方程(DAE)描述的问题,而不能解决由偏微分方程(PDE)表达的问题。为此,提出一种偏微分方程与微分代数方程的一致求解方法,利用所构建的径向基函数配点无网格法直接将偏微分方程在空间上离散成一系列的微分代数方程,然后采用成熟的微分代数方程求解器进行求解。实例结果表明,该方法在不改变Modelica语法的前提下,能较好地实现偏微分方程与微分代数方程的一致求解,且求解精度高、边界条件处理简单,有利于Modelica直接求解复杂工程系统中多领域耦合、时间域与空间域耦合的复杂问题。 展开更多
关键词 多领域统一建模 MODELICA 偏微分方程(PDE) 微分代数方程(dae)
下载PDF
一种电力系统稳定性动态分析的统一方法 被引量:3
19
作者 赵兴勇 张秀彬 苏小林 《高电压技术》 EI CAS CSCD 北大核心 2008年第10期2195-2199,共5页
为了解决电压稳定问题,基于电力系统动态分析的微分代数模型,提出了一种有效的动态稳定分析和失稳类型判别方法。利用带预测-校正步骤的延拓算法追踪平衡解流形,并采取考虑平衡解流形曲率大小的自适应策略控制步长,在平衡解流形曲率较... 为了解决电压稳定问题,基于电力系统动态分析的微分代数模型,提出了一种有效的动态稳定分析和失稳类型判别方法。利用带预测-校正步骤的延拓算法追踪平衡解流形,并采取考虑平衡解流形曲率大小的自适应策略控制步长,在平衡解流形曲率较小处采用较大步长,而在平衡解流形曲率较大处采用较小步长;在计及元件动态特性的基础上,利用小扰动法在每个平衡点分析电力系统的动态稳定性,并用数值摄动法计算状态矩阵;利用状态变量的模式参与因子判断系统的动态失稳类型。使用本文所提方法对New England 10机39节点系统进行了仿真分析,实验结果证明了本方法的有效性和实用性。 展开更多
关键词 微分代数模型 动态稳定 小扰动法 延拓法 模式参与因子 自适应控制
下载PDF
约束多体系统动力学分析的改进的离散零空间算法 被引量:3
20
作者 刘颖 马建敏 《计算力学学报》 CAS CSCD 北大核心 2013年第4期496-501,共6页
通过对已有离散零空间矩阵计算方法的改进,构造了改进的离散零空间等效变换公式,该公式可不依赖于特定的积分方法,能简洁、方便的与多种数值积分方法相结合。基于改进公式,提出了改进的离散零空间算法框架,并将该框架与一般变分积分法结... 通过对已有离散零空间矩阵计算方法的改进,构造了改进的离散零空间等效变换公式,该公式可不依赖于特定的积分方法,能简洁、方便的与多种数值积分方法相结合。基于改进公式,提出了改进的离散零空间算法框架,并将该框架与一般变分积分法结合,构造了约束多体系统动力学分析的改进的离散零空间算法。通过曲柄滑块机构的数值实验,验证了改进的离散零空间等效变换公式的正确性,示例了其与数值积分算法的良好结合性,说明了改进算法的可行性和有效性。 展开更多
关键词 约束多体系统 微分代数方程 离散零空间 变分积分法 约束违约
下载PDF
上一页 1 2 3 下一页 到第
使用帮助 返回顶部