微分代数方程

反应精馏（ReactiveDistillation，简称RD）是化工过程强化的重要方法之一，其数学模型一般为一具有强非线性的微分代数方程组，用传统方法进行数值模拟较为困难。

Reactive distillation is one of the important methods of process strengthening in chemical engineering .

连续部分利用重新定义的便于描述微分代数方程的连续Petri网，对应于位于远端的移动机器人。

By redefining the continuous Petri nets , we use it to describe the differential equations of mobile robot .

求解延迟微分代数方程的多步Runge-Kutta方法的渐近稳定性

Asymptotic Stability of Multistep Runge-Kutta Methods for Delay Differential Algebraic Equations

针对高阶（k≥2）微分代数方程系统的归约问题，给出并证明了它的一类新的归约方法。

Aimed at the problem of the differential-algebraic systems with higher index ( k ≥ 2 ), a new explicit method of its reduction is given .

非线性RK方法求解微分代数方程

Nonlinear Runge-Kutta methods for solving differential-algebraic equations

BDF方法解常系数微分代数方程的稳定性分析

Analysis of BDF Method Solving Linear Constant Coefficient Differential Algebraic Equations ′ Stability

延迟微分代数方程（DDAEs）广泛出现于科学与工程应用领域。

Delay differential algebraic equations arise in a wide variety of scientific and engineering applications .

基于条件建模的微分代数方程（DAE）在梯度上的非连续性给动态优化求解带来了很大的挑战。

Conditional model based on differential-algebraic equations ( DAE ) includes non-continuous gradients , causing huge difficulty of solving dynamic optimization problem .

本文将多步RungeKutta方法应用于求解线性常系数延迟微分代数方程，讨论了该方法的渐近稳定性。

In this paper , we apply multistep Runge-Kutta methods to sytems of linear const coefficient delay differential algebraic equations , and investigate the asymptotic stability of multistep Runge-Kutta methods .

本文将块方法和多步Runge-Kutta方法应用于线性常系数延迟微分代数方程，证明了在一定条件下A-稳定的块方法和多步Runge-Kutta方法在求解这类系统时，数值解是渐近稳定的。

This paper applies block methods and multistep Runge-Kutta methods to systems of linear delay differential algebraic equations . For A-stable block methods and multistep Runge-Kutta methods with some conditions , the numerical solution is asymptotically stable .

最后我们分析了延时微分代数方程的渐近稳定性和连续型龙格库塔方法用来求解DDAEs的渐近稳定性。

Finally , the asymptotic stability of the delay differential-algebraic equations and the continuous Runge-Kutta methods which is used to solve them are studied .

给出了保证Runge-Kutta方法对微分代数方程是正则的条件，证明了Runge&Kutta方法是正则的充要条件是折叠方法是正则的。

The conditions that guarantee regular properties of Runge-Kutta method for differential - algebraic equation are considered . It is proved that the Runge - Kutta method for differential - algebraic equation is regular if and only if the fold method is regular for differential - algebraic equation .

延迟微分代数方程（DDAEs）是具有时滞影响和代数约束的微分系统，广泛的应用于电路分析，计算机辅助设计，多体力学系统的实时仿真，化学反应模拟，最优控制等科学与工程应用领域。

Delay differential algebraic equations ( DDAEs ), which have both delay and algebraic constraints , arise in a wide variety of scientific and engineering applications , including circuit analysis , computer-aided design and real-time simulation of mechanical ( multibody ) systems , chemical process simulation and optimal control .

一阶微分代数方程组的相容性的讨论

Discussion on the compatibility of a class of mixed differential-algebraic equations

线性多步法求解广义中立型滞时微分代数方程组的渐近稳定性（英文）中立型时滞抛物偏微分方程组解的振动性

Asymptotic Stability of Linear Multistep Methods for Generalized Neutral Delay Differential-Algebraic Equations

约束保守系统导出了微分代数方程，其数值求解总是采用差分法。

The conserved constrained dynamical system derives to differential-algebraic equation .

讨论用迭代方法求解微分代数方程。

Iterative methods for differential - algebraic systems are considered .

微分代数方程系统标准奇异点的一个充分必要条件

Sufficient and necessary condition for the standard singular point of the differential-algebraic system

块隐式单步方法求解一类延迟微分代数方程

Blocks implicit one-step methods for a class of DDAEs

一类延迟微分代数方程的单支方法的数值分析

Numerical Analysis of One-Leg Methods for a Class of Delay Differential Algebraic Equations

一类非线性微分代数方程系统的线性化解耦控制

Linearization and Decoupling Control for a Class of Nonlinear Differential algebraic Equation Systems

微分代数方程的一类并行算法

A Class of Parallel Algorithms for Differential Algebraic Equations

非线性微分代数方程的一种离散波形松弛算法

Discrete Waveform Relaxation Method of Nonlinear Differential-Algebraic Equations

给出了一种能有效求解反应精馏微分代数方程组模型的数值算法。

An efficient numerical algorithm for a differential-algebraic system model of reactive distillation is given .

微分代数方程系统的一类新的归约方法

New reduction method for the differential-algebraic system

预测校正公式求解指标2微分代数方程

Predictor-corrector formula for solving Index-2 differential-algebraic equations

考虑线性多延迟微分代数方程θ-方法的渐近稳定性。

Asymptotic stability of θ - methods for linear differential-algebraic equations with several delays is considered .

讨论了广义中立型滞时微分代数方程组理论和数值解的渐近稳定性。

The asymptotic stability of analytical and numerical solutions of generalized neutral delay differential-algebraic equations was discussed .

该方法先将多体动力学方程转化为2阶微分代数方程，并与位移约束方程联立；

Firstly , the equations of motion are converted into DAE with index-2 and the displacement constraint equation remains .

对于微分代数方程的数值试验从另一个侧面证实了所构造方法是高效的和稳定可靠的。

The numerical experiment of the differential-algebraic equations confirms that the constructed methods are efficient and reliable from the other aspect .