查询词典 approximation methods in physics

In Chapter 2, starting from the basic fractional ordinary differential equations,weapply a high order approximation of fractional derivative advanced by Lubich to frac-tional differential equation, construct a high numerical difference scheme to solve thefractional differential equation, present error analysis of the algorithms theoretically,and prove the consistency ,convergency and stability.

接下来的第二章中，首先从基本的分数阶常微分方程出发，对Lubich提出的一个关于分数阶导数的高阶近似，将其应用于分数阶微分方程，构造高阶数值差分格式来进行分数阶微分方程的数值求解，并在理论上给出这一算法的误差分析，证明了它的相容性，收敛性和稳定性。

It is helpful for us to construct difference approximation schemes for HJ equation with aids of schemes for conservation laws.

众所周知，即使在初值条件0是充分光滑的情况下，一般来说，虽可以得到式(1 )的连续解，但其解的导数却是间断的。

Apply the thought of differential and integral calculus to the problem of global optimization, imitate the algorithm of digital approximation of definite integral and construct a category of algorithms that can solve global optimization with great brevity and utility.

把微积分的基本思想应用到最优化问题中，仿照定积分的数值逼近算法构造出一类简洁实用的全局优化算法-积分选择算法。

For example differential calculus does a great deal with linear approximation to functions.

例如微分做了大量的线性近似的职能。

Space fractional differential equation ; finite difference approximation ; stability ; convergence

空间分数阶微分方程；显式有限差分格式；隐式有限差分格式；稳定性分析；收敛性分析

The boundary value problem for first-order differential equations with a parameter refers to the finite solution condition of equation which includes unknown quantity and its first-order derivative that not only relies on interval value but also relies on the parameter of the equation,which is always settled by fixed point theory or successive approximation method.

含一个参数的一阶微分方程边值问题是指：含有未知量及它的一阶导数的方程的定解条件不仅依赖于在区间端点的取值，而且依赖于方程中的参数。通常它用不动点定理或逐步逼近法来解决。

In this paper, the theoretical model of CQI is described in an atom-diatom system in the condition of the molecular beam, based on the first-Born approximation of time dependent perturbation theory, taking into accounts the anisotropic Lennard-Jones interaction potentials. The method of observing and measuring correctly the differential interference angle is presented. The relation between differential and parameter, velocity is obtained. The relation of the integral interference angle and temperature is discussed.

文中利用一阶含时波恩近似和L-J相互作用势，建立了原子-双原子分子碰撞系统转动传能的量子干涉模型，描述了观察和测量微分干涉角的方法，得到了微分干涉角与碰撞半径和碰撞速度间的关系，同时也得到了积分干涉角和实验温度的关系。

The differential and partial wave scattering cross sections of Ne-H2(D2,T2) collisions have been calculated by close-coupling approximation method using Tang-Toennies potential model at the incident energy of 83.8 meV.

使用密耦近似（Close-Coupling）方法、采用Tang-Toennies势模型计算了惰性气体原子Ne与H2分子及同位素D2分子在碰撞能量为83.8 meV时的微分散射截面及分波截面，并与实验值和文献值进行比较。

The fine structure Hamiltonian for Hydrogen-like atoms is derived using the nonrelativistic approximation of the Dirac equation for one electron moving in the Coulomb field.

从Coulomb场中运动的电子的Dirac方程出发，取其非相对论极限导出了类氢离子的精细结构哈密顿的表达式。

A parallel algorithm for certain real symmetric block-tridiagonal linear systems on distributed-memory multicomputers is proposed. This algorithm is based on the block factorization of the coefficient matrix. This algorithm is used to solving the block-tridiagonal linear systems resulted from the finite difference approximation to Poisson's equation with Dirichlet boundary conditions. Then we get a parallel algorithm which speedup tends to linear speedup.

7研究了一类实对称块三对角线性方程组的分布式并行求解，提出了一种基于块矩阵分解的高效分布式并行算法，将其应用于求解带Dirichlet边界条件的Poisson方程导出的块三对角线性方程组，得到加速比趋于线性加速比的分布式并行算法，理论上说，这也是并行算法的理想情况。

We have something to do in the new stage.

在这段崭新的时期中，我们有一些要做的。

The difference between tourism decision-making under uncertainty and risky tourism decision-making is indistinctive.

其中不确定性旅游决策和风险旅游决策的界线比较模糊，两者的区分是相对的。