近似偏微分

To solve the B-Ss pricing formulas,there are many popular methods now,such as partial differential equation,analytical approximation,binomial tree methods,finite difference method and Monte-Carlo simulation.

对于Black-Scholes期权定价模型，如今比较流行的定价方法有偏微分方程、解析近似方法、二叉树方法、有限差分方法和Monte-Carlo模拟等。

Homotopy perturbation method; MOL method; nonlinear partial differential equation; approximate solution

基础科学，数学，数学分析同伦摄动法；直线法；非线性偏微分方程；近似解

Meanwhile, many new perturbed PDEs in science and technology need us to seek out approximate solutions.

同时随着科学技术的发展，出现了一些扰动的偏微分方程，需要我们去寻找它的近似解。

Firstly, an overview is given on the wave equation issue, its solution, along with the historical and present studies of computability theory.

随着计算机科学的快速发展，应用计算机来给出非线性偏微分方程的解析近似解在理论上已成为可能。

The maximum principle of the optimal control for the stochastic systems described by Zakaj stochastic partial sifferential equationis proved by approximately minimum point theorem of E. Ekeland. The convexity and compactness of the set of control values is not assumed, and it is not necessary for the maximum principle about differentiability in control variables included in drift term of the stoch astic system and the integrand in index functional, and costate process satisfies the stochastic partial ...

在不假便定控制变量取值的集合是凸的和紧的，不要求随机系统的漂移项和指标泛函的被积函数关于控制变量具有可微性的情况下，用E，Ekeland的近似极小点定理证明了Zakai随机偏微分方程描述的随机系统的最优控制的最大值原理，和用很简洁的方法证明了协态过程满足一个随机偏微分方程。

The governing equation of in-plane vibration of cable-restraint system is derived by means of D'Alembert principle, and then those partial differential equations are transformed into a set of ordinary differential equations by Garlerkin method. The method of Runge-Kutta integration is applied to solve the equation. The simulation analysis is made to prove that this vibration control has obvious damping effects and then the influence of cable tension, support mass, natural frequency and spring stiffness on the damping are discussed. Eventually, the approximate analytic solution of the optimum damping parameter is obtained to provide a simple and effective reference and design method for the engineers.

通过D'Alembert原理建立拉索－弹性约束系统振动方程，通过Galerkin方法将偏微分方程转化为常微分方程，应用龙格－库塔积分法求解方程；经过仿真分析，验证了该振动控制具有明显的减振效果，并且讨论了初始拉力、支座质量、振动频率及弹簧刚度对减振效果的影响；最后给出了计算最优阻尼参数的近似解析式，为工程师提供了简便有效的参考依据及设计方法。

Beginning with a general mean function, the model analyzes the distance between the arithmetic average and geometric average by Taylor's expanding.

第二章介绍了亚式期权定价研究中的市场结构、一般原理和若干重要的定价方法：PDE偏微分方程法；埃级沃斯级数展开近似定价；倒数分布近似定价；条件期望近似定价；执行价格调整近似定价，这些方法使亚式期权的定价得到了很大的发展。

However, the solutions of the Cauchy problem of the nonlinear hyperbolic system generally develop singularities in finite time even if the initial data are small and smooth.For this reason, solutions must be found in the space of discontinuous functions. Therefore, one can not directly use the classical analytic techniques that predominate in the theory of partial differential equations of other types. Instead, we construct approximate solutions via the singular perturbation methods. By using the compactness of the approximate solutions, we can obtain the existence of the solutions of original system.

然而一般而言，即使是在初值很小且光滑的情况下，非线性双曲型守恒律的Cauchy问题的解在有限时间内也会出现奇异性，为此，我们必须在不连续函数空间中寻找上述问题的解，因此对这类问题的研究，我们也不可能直接利用在其它类型的偏微分方程中占主导地位的解析方法来解决问题，而是通过奇异扰动法构造近似解，由近似解的紧性得到原问题解的存在性。

Using PH linearization ,the nonlinear partial differential equation was transformed into linear partial differential equation,and then,by introducing a complex function,it was further transformed into a set of two linear differential equations.

应用 PH线性化方法，将非线性偏微分方程转化为线性偏微分方程，引入复函数将复常数偏微分方程变为两个线性实常数微分方程组，并采用小参数迭代法进行求解，近似求得了螺旋槽内气体动压分布的解析解。

Different low-spetral models are used to discuss the variations of the equilibrium states, with the results that the multiple features of equilibrium saltes depend heavily on the truncations of the spectra and the low-spectral model has obvious shortcomings in solving non-linear equations, suggesting that one has to be very careful to employ highly truncated low-sp...

结果显示，平衡态的特性严重地依赖于谱的截断，显示出低谱模式在求解非线性方程中的缺陷，说明用高截断的低谱模式去近似偏微分方程需要特别小心。

As she looked at Warrington's manly face, and dark, melancholy eyes, she had settled in her mind that he must have been the victim of an unhappy attachment.

每逢看到沃林顿那刚毅的脸，那乌黑、忧郁的眼睛，她便会相信，他一定作过不幸的爱情的受害者。

Maybe they'll disappear into a pothole.

也许他们将在壶穴里消失