| 1. | The precisions and the applicable ranges of the modified rks , pr and pt equation are very similar to those of the original equations
用该式改进的rks 、 pr和pt方程在精度与适用范围方面均与原方程十分相近。 |
| 2. | For the initial value with later precision , it is shown by the actual nonlinear function examples that we can still get the precise original solutions by homotopy nonlinear ls method
算例表明，对于精度较差的初始值，算法仍能精确地收敛到原方程的参数估值。 |
| 3. | Lagrange multiplicator method is introduced in the numerical computation to release the constraint . galerkin method based on the variation principle is used to solve differential and integral equations
Galerkin方法是基于变分原理基础上的一种把微分方程或积分方程转化为等价的变分方程，通过离散变分方程求原方程数值解的方法。 |
| 4. | At present , most studies are linked to the semi - discrete scheme and the one - dimensional spatial variable . but there are very few studies about the full - discrete scheme and the higher dimensional spatial variable . furthermore , the former ca n ' t be extended directly to the latter
目前，大多数科研成果只限于对原方程是半离散和空间变量是一维的情况，对全离散格式和高维情况研究甚少，而后者并不是前者的平行推广。 |
| 5. | ( 3 ) 3 - d boussinesq equations without viscosity term ( that is 7 = e = 0 in the problem ( * ) ) - firstly , we obtain the approximate solutions by the regalarizing method and prove the local existence of the classical solution for original equations by the convergence of the approximate solutions
( 3 )三维无粘boussinesq方程组(即问题( * )中= = 0 ) 。通过正则化方法得到原方程的逼近解序列，并通过研究逼近解序列的收敛性质证明了原方程古典解的局部存在性。 |
| 6. | Adding boundary conditions in whole equations in the wavelet galerkin method frequently does with its of differential equations . the result can derive by solving transcendental equation , which make unknow quantity number and the number of system of equation become nonuniformity
经常采用的小波galerkin方法对微分方程边界条件的处理，均是将边界条件作为附加方程补充到整体方程中，从而求解超越方程组得到原方程的解，这导致了求解过程出现的方程组个数与未知量个数不一致。 |
| 7. | For scalar equation and system of equations , we build different ghost fields , translate one equation ( system ) into two equations ( system ) . we still use high resolution shock capturing method to compute the two equations ( system ) ; level set equation is used to track the interface , and the result of original equation ( system ) is determined by the level set function . thus , we eliminate the numerical dissipation which high resolution shock capturing method cannot avoid near the interface , and the resolution is enhanced
对标量守恒律方程、守恒律方程组分别构造了一种虚拟区域，将一个方程(组)转化成两个方程(组) ，对这两个方程(组) ，我们仍然使用高分辨率激波捕捉格式，而levelset方程用来追踪间断的位置，原方程(组)的解最后由levelset函数决定：这样做弥补了高分辨率激波捕捉方法在间断附近发生数值耗散的缺陷，提高间断处的分辨率。 |
| 8. | Exact solutions are derived for the forced vibration of plate on elastic foundation to moving loads , which is based upon the use of the 2 - d fourier transforms to the motion equations and boundary conditions . following a series of deduction , a calculation programme by the methods of numeric integration in fortran is provided
由系统的运动方程出发，利用界面连续条件，运用积分变换方法对原方程及边界条件进行了二维fourier积分变换，把偏微分方程组变成常微分方程组，求出加铺层板系统在移动荷载作用下的挠度解析解。 |
| 9. | ( 4 ) due to the imperfectness of solving the fuzzy equations , complexity in computation of fuzzy finite element equations and imbalance in the two sides of fuzzy finite element equations while the solution was lead back to the original equations , the fuzzy finite element method based on fuzzy coefficient programming was
( 4 )针对模糊方程组的求解技术尚不完善，模糊有限元方程组的计算存在着计算量大且将得到的解代回原方程时方程组的两边不平衡等问题，提出了基于模糊系数规划的模糊有限元求解方法。 |
| 10. | Based on the normal form obtained above , a global perturbation method is utilized to give the analysis for the global bifurcations and chaotic dynamics of the rotor - ambs system . the global bifurcations analysis indicates that there exist the heteroclinic bifurcations and the silnikov - type homoclinic orbit in the averaged equations
利用全局摄动法研究了电磁轴承-转子系统的全局分叉和混沌动力学，利用数值模拟方法分别对平均方程和原方程进行了分析，得到了的描述系统混沌运动的相图和波形图，从而验证了理论结果的正确性。 |
