待定系数法

Firstly,the differential equation with parameters is given,at the same time,in order to let the truncation error of differential equation reach O(Δt~2+Δx~4) as high as possible,the method of undetermined coefficent is used to appropriately select the expression of these parameters.Secondly,the stability condition of the scheme derived is given by using the Fourier method of stability analysi...

首先给出了含参变量的差分方程，并用待定系数法适当地选取了这些参数的表示式，以使差分方程的截断误差阶尽可能高地达到了O(Δt2+Δx4)；其次用稳定性分析的Fourier方法给出了所得格式的稳定性条件；然后给出了确定差分格式中参数的两种方法，得到了一个稳定性条件为r/3的分支稳定的高精度显式差分格式；最后给出了数值例子，数值结果表明了本文格式较现有同类格式的优越性和理论分析的正确性。

The fracture problem can be solved by calculating the boundary value of a partial differential equation. By the methods of complex variable function and undetermined coefficients, the formulae for deflection, displacement, bending moment, torque, stress and strains near the crack tip are derived.

该断裂同题可化为求解一个偏微分方程的边值问题，借助复变函数方法和待定系数法，推出了裂纹尖端附近的挠度、位移、弯矩、扭矩、应力和应变的计算公式。

Special attention should be paid when we apply the decomposition method to two-point boundary value problems, it is necessary to solve a algebraic system;It should be noted that a modification of inverse operator should be made when dealing with singular boundary value problems;Laplace transform and Pade approximants can be coupled to enhance the efficiency of the decomposition method.

比如，在求解两点边值问题时就需要特别注意，这时需要采用待定系数法，最后会涉及到系数方程组的求解；在处理奇异边值问题时需要重新定义逆运算；不少研究人员还把分解方法与Laplace变换和Padé逼近相结合来进一步提高分解方法的精度。

By introducing special stress functions, we find solutions of eighth order homogeneous linear equation set with complex functions method and approach of undetermined coefficients, deduce calculation formulas of bi-material elastic constants for two dissimilar orthotropic composite materials. The expressions of stress intensity factors near finite interface crack tip subjected to symmetric loadings are derived. A engineering application numerical example is given.

通过引入特殊的应力函数，采用复变函数方法和待定系数法求解了八阶齐次线性方程组，推出了两种相异正交异性复合材料板的双材料弹性常数的计算公式，得到了受对称载荷作用的界面裂纹尖端应力强度因子的计算公式，给出了一个工程应用算例。

In this paper,the Newtonian fluid model was used to describe rheological property of the produced fluid,and motion equation of unsteady flow of Newtonian fluid in eccentric annulus with the inner cylinder reciprocating axially was transformed by means of the method of undetermined coefficients.

采用Newton流体模式描述油井产出液的流变性，利用待定系数法变换Newton流体在内管做轴向往复运动的偏心环空中非定常流的运动方程，建立给定流量下Newton流体在内管做轴向往复运动的偏心环空中非定常流的压力梯度计算公式，并利用有限体积法对压力梯度进行数值计算。

In this paper,based on the characteristic of the tridiagonal matrix,the method of hypothetical coefficient is used for the numerical solution of tridiagonal system of linear equations,this method will be compared with the LU resolving

文章将根据3对角矩阵的特征，用待定系数法求解3对角线性方程组的数值解，并与常用的LU分解法从理论分析和数据实验两方面进行比较，结果表明，两者的时间复杂性前者稍差，而精度两者则相当，最

Using many methods,such as method of completing the square,method of undetermlined coeficient etc,this paper solves the problem of integral of rational proper fraction.

利用配方法，待定系数法等方法求解有理真分式的积极分问题。

Key words: geometry; fractal; characteristic angle sequence function; method of undetermined coefficient; square wave Koch-like curve

关键 词：几何学；分形；特征角序列函数；待定系数法；Koch类方波曲线

In this paper,the kinematic equations of flow of Newtonian fluid of helical flow in eccentric annulus were transformed by the method of undetermined coefficient,the calculation formula of pressure gradient of flow of Newtonian fluid of helical flow in eccentric annulus was obtained.

本研究利用待定系数法对 Newton 流体偏心环空螺旋流动的运动方程进行了变换，得到了给定流量情况下 Newton 流体偏心环空螺旋流动的压力梯度的计算公式。

For overcome nonlinear terms of any degree in the equation, we made a proper transformation according to the structure of the equation at first, make the equations into ordinary differential equation. Then solve the ordinary differential equation exactly, by auxiliary functions method and undetermined the coefficient method and algebraic computer system Mathematica.

为了克服方程中非线性项的任意次幂，我们采用的方法是首先根据方程的特点，做适当的变换，使原问题转化为常微分方程的问题，其次对该常微分方程再进行各类变换，如辅助函数法以及待定系数法……。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。