本文试应用求解一阶线性微分方程的方法导出几类常见的函数项级数的求和公式。
The sum formulas of several kinds of ordinary series with function term are deduced by using the method of solving linear differential equation.
这些工作为格林函数快速计算方法的实现以及积分方程的矩量法高效求解打下了基础。
The derivations lay a good foundation for the efficient evaluation of Green's functions and the fast solving of scattering problems by the method of moments (MoM).
在考虑瞬态过程中动量扩散速度基础上，用拉普拉斯变换法对无限长平板突然起动瞬态动量定解方程进行了求解，并按涡量定义求出涡量分布函数。
Based on the limited momentum propagation velocity, this paper presents the solution of the transient momentum equation by Laplace transform. The distribution functions of velocity and eddy are given.
在二粒子集团近似下导出了分子取向分布函数所满足的方程，并用迭代方法求解。
The equation of the molecular orientational distribution function was obtained by two-particle cluster approximation and solved by an iterative method.
对此，本文根据天然气流动情况，引入一线性化函数，通过求解非线性方程得到了解析解。
Therefore, this paper introduces a linearized function in light of the flow conditions of natural gas and obtains an analytic solution through solving nonlinear equations.
本文通过引入位移函数使得立方准晶的轴对称弹性问题化为求解一高阶偏微分方程。
Axisymmetric elasticity problem of cubic quasicrystal is reduced to a solution of a partial differential equation with higher-order by introducing displacement function.
本文研究了散射相函数的有限项的勒让德展开对于求解辐射传输方程的误差效应，提出了一个改进算法。
In this paper, the effect of Legendre expansion of scattering phase function with a finite number of terms on solving radiative transfer equation is studied and an improved algorithm suggested.
运用复变函数及积分方程方法，求解了半平面域多圆孔多裂纹反平面问题。
By using of complex variable function and integral equation method, the antiplane multiple holes and cracks problem of half plane region is considered in this paper.
这个函数求解一个标准的二次方程。
求解了运动媒质中电磁势方程的格林函数，给出了无界空间的推迟势。
Solving the Greens functions of electromagnetic potential equations in moving medium, the retarded potentials in unlimited space are obtained.
本文通过有限元法求解用流函数表示的拉普拉斯方程，进而计算轴流式机组的静态轴向水推力。
In this thesis, the Finite Element Method is applied to the solution of the Laplace equation formulated by means of stream function for the calculation of the static hydraulic thrust.
快群方程用格林函数节块法进行求解。
The fast group equation is solved by the Green's function method.
本文用压缩变挟方法，求解了函数解随自变量增加而迅速增长的一类常微分方程的边值问题。
In this paper, a kind of boundary value problems of ordinary differential equations, in which the function solutions increase rapidly, are solved by means of compressed transformation.
不用任何函数展开，通过迭代方法求解平衡态方程，得到精确的取向分布函数。
Without any functional expansions, accurate orientational distribution functions are obtained by using a newly iterative method to solve the equation of equilibrium state.
本文采用修正格林函数积分方程的矩量法数值解技术求解静电场边值问题。
A new approach to numerical solution of the boundary-value problems of static-electric fields, the Modified Green Function kernel integral equation and its moment-method solution, is presented.
利用复变函数和奇异积分方程方法，求解反平面弹性中半平面边缘内分叉裂纹问题。
The edge internal branch crack problems for half-plane in antiplane elasticity are solved with complex potentials and singular integral equation approach.
用该方法可以求解列出的电路系数函数方程找出故障元件。
With this method, we can find out the fault components by calculating the equations of coefficient function of the circuit.
然后应用数值传递函数方法对方程求解，就可以得到系统的动力、静力响应。
The equations are solved by the STFM, and the static and dynamic responses of the plane are obtained.
针对这一优化问题，通过引入非线性互补问题函数，将原优化问题转化为非线性方程组，并采用半光滑牛顿法进行求解。
By introducing nonlinear complementarity problem function, the original optimization problem is transferred equivalently to a set of nonlinear equations and solved by semi-smooth Newton method.
本文对球函数方程进行了求解，并将球函数方程的解合理地应用于角动量平方算符的本征值问题中。
The solution of spherical function is given in the paper, and it is applied reasonably in the problem of eigenvalue of angular momentum square operator.
应用改进后得到的数值传递函数方法对方程求解，就可以得到系统的动力、静力响应。
The equations are solved by the numerical SDTFM, and the static and dynamic responds of the plane are given.
重点研究了利用并矢格林函数求解同轴结构中的色散方程。
Using Dyadic Green Function, the dispersive equations of co-ordinate structures are studied in this paper.
数值实验表明，径向基函数配置点方法与正则化方法耦合能有效求解椭圆型偏微分方程反问题。
It is concluded that the radial basis function collocation techniques coupled with regularization methods could be competitive alternatives to existing methods for these problems.
由于准则方程的高次非线性和复杂性，文中利用复合函数求导法则，直接针对基本随机变量求解。
Because of the complexity and high order nonlinear property of the criterion, a derivative method for compound function is used to get reliability.
此外，利用了WENO法求解等位函数方程的空间离散项。
In addition, the WENO method may solve the space discrete items of the level set equation.
将中子伴随通量方程变换处理以后，利用格林函数节块法的原理求解中子伴随通量，以此代替过去采用最多的细网有限差分法。
A coarse mesh method, in which the theory of nodal Green's function method is adopted, is applied to get the adjoint neutron flux, after a transformation of adjoint flux equations has been made.
其次，在数值求解该组方程的过程中，未知函数裂纹表面位移差被近似为位移差的基本密度函数与多项式之积。
Then these equations are solved numerically by approximating the unknown displacement difference to a product of the fundamental density function and polynomials.
引入指数函数，将对流扩散方程变换为扩散反应方程，消除了数值求解中较难处理的对流项。
To eliminate the difficulty in dealing with convection terms, an exponential transformation function is introduced to turn the CDE into their equivalent diffusion-reaction equations (DRE).
应用格林函数方法，将波纹膜片的非线性边值问题化为非线性积分方程进行求解。
The nonlinear boundary value problem of the corrugated diaphragm reduces to the nonlinear integral equations by applying the method of Green's function.
以裂纹面上的位错函数为未知量将圆柱型界面裂纹问题化成一组奇异积分方程的求解问题。
The problem of a cylindrical interface crack is reduced to a system of singular integral equations with the aid of two unknown dislocation functions at the interface crack surface.
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