高阶方程

词组短语

equation of higher order

与高阶方程相关的网络例句 [注：此内容来源于网络，仅供参考]

The cross-high-order-cumulant such as the cross-fourth-order cumulant is firstly proposed to measure the signal and for the first time prove that the CHOC can control the non-relevant noises and Gaussian noises. And based on the cross-high-order spectral Yule-Walker equations, the sinusoidal signal matrix is decomposed by the way of singular value decomposition method.

摘 要：本文以互四阶累积量为依据，首次证明了互高阶累积量可以有效地抑制非相关噪声和高斯噪声；并在建立互高阶累积量的Yule-Walker方程的基础上，通过该矩阵的奇异值分解，建立了信号矢量空间与噪声矢量空间；首次提出了混合噪声背景下正弦参数估计的互高阶谱Pisarenko方法。

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。

Second order incident boundary condition on fixed incident boundary is derived for numerical simulations, based on the cnoidal or sinusoidal motions of wave maker paddle, which shows that the prediction with second order incident boundary condition is more accurate than the prediction with first order incident boundary condition. 2 The analytical solution for higher-order Boussinesq equations is derived and its applicable range is discussed. 3 A 2-D fully non-linear numerical model using boundary element method is developed to obtain wave forces acting on rectangular obstacle. 4 The three-dimensional fully non-linear waves are studied in a numerical wave tank using finite element method.The studies on the coupled numerical model combined Boussinesq equations with Laplace equation are following.

非耦合非线性波浪计算模型：1 根据造波板做椭圆余弦运动或正弦运动速度，推导出数值模拟波浪水槽时固定入射边界上的二阶波浪入射边界条件，数值计算结果和实验结果的对比表明采用二阶入射边界条件对波面升高的预报比采用一阶入射边界条件对波面升高的预报更为精确；2 推导了波浪水槽造波板做正弦运动所产生波浪的高阶Boussinesq方程摄动展开解析解，讨论了该解析解的适用范围；3 对整个波浪水槽应用边界元方法数值模拟了波浪对物体的非线性作用；4 用有限元法求解三维Laplace方程模拟了三维完全非线性波浪水槽。

The main contents of this course include: the elementary solution of first order differential equations, the theory of existence, uniqueness and continuity dependency of initial value problem of first order differential equations, the structure theory of higher order linear differential equation and the solution of constant coefficient equations, the structure theory of system of linear equations, basic solution matrix and the solution of system of constant coefficient equations.

本课程内容有：一阶微分方程初等解法，一阶微分方程初值问题的存在性、唯一性、连续依赖性理论，高阶线性微分方程解的结构理论和常系数方程解法，线性方程组的结构理论、基解矩阵和常系数方程组的解法。

Three elements should be calculated in first-order circuit, which can synthesise analytical solution. Second-order series RLC and parallel RLC both can be calculated by the general function, which uses the Matlab to calculate differential equations. Generally, second-order and high-order circuits use Laplace transformation to formulate circuit equation, and get analytical solution by using Laplace inverse transform.

一阶电路先计算3要素，后合成解析结果；RLC串联和并联的二阶电路采用自编的通用函数计算，自编函数采用了Matlab求解微分方程的符号运算方法；一般的二阶电路和高阶电路采用拉氏变换列写电路方程，再用拉氏反变换得到解析结果。

Firstly, by adopting the thought of Adomian's decomposition method, the generic dynamic model in mechanical systems are transformed into a standard first-orderdifferential-equations, and then the inverse operator method for the approximate analytic solution of nonlinear mechanical system is developed based on the exact solution in form.

主要研 究工作如下：利用Adomian的分解方法的思想，把机械系统中最一般的动力学模型转化为一阶标准型微分方程组，以形式上的精确解的表达式为基础构造了求解机械系统非线性模型近似解析解的逆算符方法；针对机械系统非线性模型的特点，提出了直接处理高阶方程的不降阶逆算符方法；证明了该方法的收敛性。

By transforming high - grade gentle lack one type linear differential equation into the linear differential equation of successive integral, the theory and method for the general solutions of this kind of equation are determined.

方程'+=f是高阶线性微分方程，(约定尹0)=刃，是两项和的形式，其特征是含有相同的底，导数的次数相差一阶，因此不妨定义该方程为：高阶和式次数差一型线性微分方程。

Based on this, a new WENO difference scheme which based on Dispersion-Relation-Preserving relation is developed, and representative test cases with this scheme for computational aeroacoustics problems has been implemented and compared in order to test capability of wave capturing; In addition, WENO schemes generally do not converge at high order in the presence of contact discontinuity of Euler equations, so a conservative front tracking technique coupling WENO schemes and Level Set method to simulate the translating density profile is presented here, and numerical simulation with this technique for representative test case has been implemented and results show the desired accuracy.

本文研究了高阶精度加权基本无振荡格式及其在双曲守恒律方程中的应用，在此基础上作了两个方面的工作：一是针对高频声波问题构造出一种基于保色散关系的WENO有限差分格式，并对计算气动声学问题的代表性算例进行了大量数值实验，比较了该格式捕捉波数的能力；另外，针对高阶WENO格式在处理Euler方程的接触间断时精度有所降低的问题，研究了利用界面追踪技术Level Set方法和高阶激波捕捉WENO格式相结合的一种守恒追踪方法，并且给出有代表性的密度滑移面问题的算例，得到一致高阶精度的数值模拟结果。

High order symplectic schemes of three-dimensional time-domain Maxwell's equations are constructed with symplectic integrator technique combined with high order staggered difference. The method is used to analyzing stability and numerical dispersion of high order time-domain methods and symplectic schemes with matrix analysis and tensor product.

利用辛积分技术与高阶交错差分技术，建立求解三维时域Maxwell方程的高阶辛算法；结合电磁场中的物理概念，借助矩阵分析和张量分析理论，获得高阶时域方法及高阶辛算法的稳定性和数值色散性的统一处理新方法。

In this project, we study the theory of higher order differential equations in Banach spaces and related topics. We solve an open problem put forward by two American Mathematicians and two Italian Mathematicians concerning wave equations with generalized Weztzell boundary conditions, introduce an existence family of operators from a Banach space $Y$ to $X$ for the Cauchy problem for higher order differential equations in a Banach space $X$, establish a sufficient and necessary condition ensuring $ACP_n$ possesses an exponentially bounded existence family, as well as some basic results in a quite general setting about the existence and continuous dependence on initial data of the solutions of $ACP_n$ and $IACP_n$. We set up quite a few multiplicative and additive perturbation theorems for existence families governing a wide class of higher order differential equations, regularized cosine operator families, regularized semigroups, and solution operators of Volterra integral equations, obtain classical and strict solutions having optimal regularity for the inhomogeneous nonautonomous heat equations with generalized Wentzell boundary conditions, gain novel existence and uniqueness theorems,which extend essentially the existing results, for mild and classical solutions of nonlocal Cauchy problems for semilinear evolution equations, present a new theorem with regard to the boundary feedback stabilization of a hybrid system composed of a viscoelastic thin plate with one part of its edge clamped and the rest-free part attached to a visocelastic rigid body. Also we obtain many other research results.

在本研究中，我们对Banach空间中的高阶算子微分方程的理论以及相关理论进行了深入研究，解决了由美国和意大利的四位数学家联合提出的一个关于广义Wentzell边界条件下的波动方程适定性的公开问题，恰当地定义了Banach空间中的高阶算子微分方程Cauchy问题的算子存在族及唯一族，建立了齐次和非齐次高阶算子微分方程Cauchy问题适定性的判别定理，获得了关于高阶退化算子微分方程的算子存在族、正则余弦算子族、正则算子半群、Volterra积分方程解算子族的乘积扰动和混合扰动定理，得到了关于以依赖于时间的二阶微分算子为系数的一大类非自治热方程非齐次情形下的时变广义Wentzell动力边值问题的古典解、严格解的最大正则性结果，获得了半线性发展方程非局部Cauchy问题广义解和经典解存在唯一的判别条件，从实质上推广了现有的相关结果；得到了一部分边缘固定而另一部分附在一粘弹性刚体上的薄板构成的混合粘弹性系统的边界反馈稳定化的新稳定化定理，还建立了一系列其他研究结果。

与高阶方程相关的网络解释 [注：此内容来源于网络，仅供参考]

partial derivative of higher order：高阶偏导数

高阶逻辑|high order logic | 高阶偏导数|partial derivative of higher order | 高阶偏微分方程|partial differential equation of higher order

equation of higher order：高阶方程式

equation of heat conduction 热传导方程 | equation of higher order 高阶方程式 | equation of jacobi 雅可比方程

equation of higher order：高阶方程

equation of higher degree 高次方程 | equation of higher order 高阶方程 | equation of intersector equilibrium 门部间流量均衡方程

differential equation of higher order：高阶微分方程

differential equation of first order 一阶微分方程 | differential equation of higher order 高阶微分方程 | differential equation solver 微分方程解算机

nonlinear wave equation of higher order：非线性高阶波动方程

高阶拟线性双曲方程.:Higher order quasilinear hyperbolic equations. | 非线性高阶波动方程:nonlinear wave equation of higher order | 高阶时频分布:Higher order time-frequency distribution

linear hyperbolic equation of higher order：高阶线性双曲[型]方程

高阶微分方程|differential equation of higher order | 高阶线性双曲[型]方程|linear hyperbolic equation of higher order | 高阶线性椭圆[型]方程|linear elliptic equation of higher order

partial differential equation of higher order：高阶偏微分方程

高阶偏导数|partial derivative of higher order | 高阶偏微分方程|partial differential equation of higher order | 高阶奇点|singular point of higher order

linear elliptic equation of higher order：高阶线性椭圆[型]方程

高阶线性双曲[型]方程|linear hyperbolic equation of higher order | 高阶线性椭圆[型]方程|linear elliptic equation of higher order | 高斯-若尔当消元法|Gauss-Jordan elimination

High- order Ambiguity Function：高阶模糊度函数

高精度紧致差分格式:high-order compact scheme | 高阶模糊度函数:High- order Ambiguity Function | 高阶中立型微分方程:high order neutral differential equation

singular point of higher order：高阶奇点

高阶偏微分方程|partial differential equation of higher order | 高阶奇点|singular point of higher order | 高阶微分|differential of higher order