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龙格-库塔方法
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  “龙格-库塔方法”译为未确定词的双语例句
    The stability of Runge-Kutta methods for nonlinear MDDEs
    非线性多延迟微分方程龙格-库塔方法的稳定性
短句来源
    (2) Sufficient conditions of symplectic,(φ~(-1))-symmetric and algebraically-stable MRRK which are based on the modified W-transformation,are presented.
    (2)基于修改的W-变换我们分别得到了辛、(φ~(-1)-对称和代数稳定的多旋转龙格-库塔方法的充分条件。
短句来源
    Our methods of implicit symplectic ,(φ~(-1))-symmetric,algebraically-stable and implicit multi-revolution Runge-Kutta(MRRK)methods of high order are,when N→ ∞, the classic methods of symplectic,symmetric,algebraically-stable and implicit Runge-Kutta methods of high order obtained by Hairer and Wanner(1981),Sun (1993),Chan(1990)and so on.
    当N→∞时,我们获得的高阶隐式辛、(φ~(-1)-对称和代数稳定的多旋转龙格-库塔方法就是Hairer和Wanner(1981)、Sun(1993)、Chan(1990)等人所获得的经典的高阶隐式辛、对称和代数稳定的Runge-Kutta方法。
短句来源
    In comparison with the symplectic perturbed collocation method, we give the numerical experiments for the equivalent symplectic Runge-Kutta method and another two non-symplectic methods.
    众所周知,理论上等价并不意味着数值上等效,因此我们也给出了等价的辛龙格-库塔方法的数值计算。
短句来源
    It shows that a remarkable advantage of the symplectic methods applied to the Schrodinger equation is the precise preservation of charge conservation law.
    为了比较,我们还给出了同阶的非辛算法的数值模拟,从而得到辛摄动配置算法和其在理论上等价的辛龙格-库塔方法在数值上的等效性以及辛算法在数值计算中的优越性。
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  method of curve fitting
The dissociation energy is estimated to be 7.70±0.19 eV by the method of curve fitting using the five parameter Hulburt-Hirschfelder's function.
      
The ground-state dissociation energies evaluated by the method of curve fitting using the H-H function agree well with the values reported earlier.
      
Regression lines were estimated with use of the least-squares method of curve fitting.
      


In this paper several numerical methods for calculating nonlinear vibrations are compared with each other.Results show that the fourth-order Runge-Kutta method is more accurate and effective than the constant-average-acceleration method and the linear acceleration method.Using linear interpolation can be calculated periods of periodic vibrations accurately, and with the aid of numerical integration the amplitudes of each harmonic vibrations can be calculated.The calculations help us analyse the numerical results...

In this paper several numerical methods for calculating nonlinear vibrations are compared with each other.Results show that the fourth-order Runge-Kutta method is more accurate and effective than the constant-average-acceleration method and the linear acceleration method.Using linear interpolation can be calculated periods of periodic vibrations accurately, and with the aid of numerical integration the amplitudes of each harmonic vibrations can be calculated.The calculations help us analyse the numerical results more thoroughly.In calculating the amplitudes of each harmonic vibrations, the results of numerical integration method and those of perturbation method are very coincidental with one another.

本文对求解非线性振动的几种数值方法进行了比较,结果表明,在平均加速度法、线性加速度法、四阶龙格库塔方法中,以四阶龙格—库塔法精度高,速度快。对周期性振动,可用线性插值的方法求得周期的准确值,并可用数值积分的方法求得各阶谐振动的大小,这有利于对数值结果进行深入分析。数值积分求得的各阶谐振动大小与摄动法相比较可以发现,二者的结果相当吻合。

In this study the construction of the yield component systemis regarded as the grey dynamic procedure in which all the yield ele-ments are related to each other. Based on the data generation and model-building theory of the grey system, the yield component grey systemmodel is constructed using the data from separate seeding date tests atequal intervals in a year. The impact of different seeding dates on theyield component system is simulated by Runge-Kutta method .The re-sults are satisfactory.

本文将产量结构系统的建成看成是各个产量要素相互关联的灰色动态过程,按照灰色系统的数据生成及建模理论,采用年内等间隔分期播种试验的产量结构资料,建立了产量结构灰色系统模型,并用龙格-库塔方法模拟了不同播种期对产量结构系统的影响,取得了较好的效果。

Inverse operator theory method (IOTM) has developed rapidly in the last few years. It is an effective and useful procedure for quantitative solution of nonlinear or stochastic continuous dynamical systems. Solutions are obtained in series form for deterministic equations, and in the case of stochastic equation it gives statistic measures of the solution process. A very important advantage of the IOTM is to e-liminate a number of restrictive and assumption on the nature of stochastic processes. Therefore, it...

Inverse operator theory method (IOTM) has developed rapidly in the last few years. It is an effective and useful procedure for quantitative solution of nonlinear or stochastic continuous dynamical systems. Solutions are obtained in series form for deterministic equations, and in the case of stochastic equation it gives statistic measures of the solution process. A very important advantage of the IOTM is to e-liminate a number of restrictive and assumption on the nature of stochastic processes. Therefore, it provides more realistic solutions. The IOTM and its mathematics-mechanization (MM) are briefly introduced in this paper. They are used successfully to study the chaotic behaviors of the nonlinear dynamical systems for the first time in the world. As typical examples, the Lorentz equation, generalized Duffing equation, two coupled generalized Duffing equations are investigated by the use of the IOTM and the MM. The results are in good agreement with ones by the Runge-Kutta method (RKM). It has higher accuracy and faster convergence. So the IOTM realized by the MM is of potential application valuable in nonlinear science.

逆算符方法是近年来发展起来的一种有效定量求解非线性和随机性连续方程的方法,对于确定论方程得到级数形式的逼近解,对随机方程可以得到解的随机测度。该法无需任何假设和限制,因此它能提供更真实的解。文内首先简介逆算符方法及如何实现对它的数学机械化;然后用逆算符方法研究了三个典型的非线性方程:Lorentz方程,广义Duffing方程和双耦合广义Duffing方程。用四阶龙格-库塔方法进行比较,说明逆算符方法比龙格-库塔方法具有更高的精度和更快的收敛性。该工作是首次把逆算符方法应用于混沌行为的研究,并将此法在微机上实现了数学机械化。该法有很大的普适性,特别适用于对复杂问题的定量计算,大有应用和发展前途。

 
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