Runge

The program adopted the improved augmented matrix method. Based on example verification and practical application and through statistics it demonstrated that the improved augmented matrix method is 4 to 10 times faster than the fourth order Runge-Kutta method with accuracy ensured and fine stability resulted.

它采用了改进增广矩阵算法，经考题验证和实际应用证明，在保证精度的前提下，改进增广矩阵法比四阶Runge-Kutta法提高运算速度4～10倍，且精度高、稳定性好。

Using unsteady Euler codes to solve aerodynamic loads, coupled with structural equations, using improved Runge-Kutta time marching method, the flutter of one-degree of freedom-buzz that often occurs in transonic flows is studied in time-domain.

运用非定常Euler方程求解气动力，耦合结构运动方程，采用改进的四步龙格-库塔推进方法，在时间域内研究了音速附近发生的单自由颤振问题。

Linear multi-step method, θ-method, and Runge-Kutta method are effectively numerical methods for solving DDEs and NDDEs.

我们知道，求解各类延迟微分方程，线性多步法，θ-方法和Runge-Kutta方法都是非常有效和常用的方法。

For multi-degree nonlinear mechanical model of single phase transformer windings, the time domain response and the relation between the response and various parameters are obtained by Runge-Kutta method.

对于典型的单柱式变压器线圈系统建立了非线性多自由度模型，进行了短路响应数值分析，得出了响应特征及其和变压器各参数之关系。

The diameter of a fixed-bed adiabatic reactor, height of catalyst bed and catalyst loading were calculated by using Runge-Kutta numerical solution method.

采用龙格－库塔数值解法，计算了不同设计方案时，固定床绝热反应器的直径、催化剂床层高度及装量；

An explicit high-order Runge-Kutta method to solve the motion differential equations for accurate cloth simulation is presented. By use of embedded cash-karp runge-kutta formula, the algorithm is further optimized on the side of auto-adjustment for step size and error control.

针对具有高精度要求的织物动态仿真，提出利用显式Runge-Kutta高阶方法解决仿真过程中运动微分方程的求解问题，并采用内嵌的Cash-Karp计算格式，从自动调整步长和控制精度两方面优化算法。

Efficient implementation of fully implicit Runge-Kutta methods and its application to time-discretization PDEs

全隐Runge-Kutta法的有效实现及其在偏微分方程时间离散化中的应用

Results Taking the gyrostabilizer system of ×× satellite for example, the dynamic equations were solved under giving initial conditions using the Runge-Kutta numeric method, investigate the dynamic optimization design for the gyrostabilizer system.

结果以××航天器天线姿态稳定系统为例，在给定初始条件下用Runge Kutta数值方法对系统的动力学模型进行了数值仿真，从而为陀螺机构的动力学优化设计奠定了基础。

The second order stochastic Runge Kutta algorithm for systems driven by a single additive noise is generalized, which makes it more suitable for complex situation.

推广了单噪声驱动系统的二阶随机龙格库塔数值模拟算法，使之适用于关联白噪声和色噪声共同驱动的系统这一更为复杂的情况。

The Runge-Kutta method is utilized to obtain the relationship between the angle as well as the angular velocity and time in the case of the slide way structure.

基于Runge-Kutta方法得到了在滑道式俯仰角控制结构下分离过程中模型角度、角速度与时间之间的对应关系。

Using fourth-order Runge-Kutta method for the corresponding input nonlinear systems, and modeling using simulink comparison.

用四阶龙格库塔法求非线性系统的输入相应,同时用simulink建模比较.

This paper finally to synchronous generator of three-phase short-circuit as example, using four order Runge Kutta method to simulate synchronous generator three-phase short-circuit fault phenomenon, and the real-time simulating and analyzing the simulation step on the single DSP, obtained the ideal simulation step.

文章最后以同步发电机三相短路故障为例，采用四阶龙格库塔法在单台DSP上进行了实时仿真并对仿真步长进行了比较分析，得出了实时仿真较为理想的仿真步长。

The characteristic method and the classical Runge-Kutta method were adopted for simulation.

计算方法采用带内插的特征线方法和四阶龙格库塔法.

It uses the Runge-Kutta method to calculate manipulation of the mathematical model of the equations of motion. "Yu-Kun" turning simulation uses Matlab mathematical language.

用龙格&库塔法对操纵运动方程的数学模型进行计算，同时采用Matlab数学语言对育鲲轮的旋回运动进行模拟仿真。

The set of ordinary differential equations is integrated with the Runge Kutta Gill method according to the required time accuracy. The same spatial discretion is adopted for the Poisson equation. The successive over relaxation method is used.

随时间变化的发展方程采用Runge Kutta Gill法求数值解，在空间上离散的Poisson差分方程采用超松弛迭代法求解。

Multistep Runge-Kutta Type TVB Time Discretizations

多步Runge-Kutta型TVB时间离散

Finite volume discretization is used in spatial form and Runge-Kutta method in time marching direction.

空间方向用有限体积离散，时间方向用Runge－Kutta法推进。

The Runge-Lenz Vector and the Perihelion Precession of Mercury Orbit

Runge-Lenz矢量与水星近日点进动

General Purpose Simulation Program Based on Runge-Kutta Method for Linear Control System

基于龙格&库塔法的线性控制系统通用仿真程序

Numerical Solution of Higher Order Discontinuous Nonlinear Ordinary Differential Equation System ( Variable Step Length-Runge Extrapolation-Extension Method )

高阶非线性间断常微分方程组的求解 ( 变步长RUNGE外推外延法 )

A numerical program for one-dimensional nucleating flow by the fourth order Runge-Kutta scheme is also developed and slip factor B is introduced to simulate the flow when the velocity difference between two phases exists.

编制了采用四阶Runge-Kutta法的一元凝结流计算程序，并在一元动量方程中引入了滑移因子B，以模拟汽液两相速度差存在时的流动。

In the condition of two types of acceleration induced by the nuclear explosion, the isolation properties of double mass spring system are studied by the Runge Kutta method based on vibration dose value ( VDV) criterion.

根据振动剂量值（VDV）隔震标准，采用Runge-Kutta法研究了双层线性隔震系统在核爆炸产生的两类冲击震动作用下的隔震性能。

The three-layer model of thermomechanical loading is reduced to a set of the ordinary differential equations of one order. Numerical solution algorithms are developed based on the classical fourth order Runge-Kutta method.

热机械加载三层细观力学模型归纳为一阶常微分方程组的初值问题，在考虑数值求解的方法时采用了经典的4阶Runge-Kutta法。

The equation was solved with both the time finite element method and the fourth order Runge-Kutta method.

分别用时间有限元方法和四阶的Runge-Kutta方法对方程进行了求解。

Considered terrain condition, a mathematical model of droplet random splash was proposed, and the corresponding differential equation was set up and worked out by Runge-Kutta and Monte-Carlo method.

在考虑地形的条件下，研究了挑流水舌撞击尾水时水滴随机喷溅特性，建立了水滴随机碰溅的数学模型，提出了地面降雨强度的求解方法。

For example Runge-Kutta method, 0-method, one-leg methods, linear-multi step methods, etc. However, these traditional methods also have many shortcomings, such as low precision, slow convergence, to solve some special problems may have difficult.

但这些传统方法也存在着很多不足，比如精度低、收敛慢，对一些特殊的问题求解比较困难等。

The numerical calculation results show that accuracy and efficiency of the second-order exponential time differencing Runge-Kutta method are better than those of forth-order traditional Runge-Kutta method.

数值计算结果表明，对于非线性动力学系统，二阶指数时程差分Runge Kutta法在计算效率和精度上要优于四阶传统Runge Kutta法；

Research on Iterative Runge-Kutta Methods for DAEs

关于微分-代数系统的Runge-Kutta迭代方法的研究

The partial pressure profile of butene-1 in catalyst pore was calculated by the Runge-Kutta method.

用Runge－Kutta方法计算了丁烯－1在催化剂孔内的分压分布。

A three-ball model is suggested to simulate balancing the effectiveness and mechanism caused by the liquid in the equilibrium ring. The numerical results of the complicated vibration equations of the tub are obtained by using Runge-Kutta method.

为研究平衡环中盐液的平衡作用和机理，提出了模拟平衡环的三球模型，用Runge-Kutta法得到了桶体振动方程的数值结果。