如果你也在 怎样代写有限元方法finite differences method 这个学科遇到相关的难题，请随时右上角联系我们的24/7代写客服。有限元方法finite differences method在数值分析中，是一类通过用有限差分逼近导数解决微分方程的数值技术。空间域和时间间隔（如果适用）都被离散化，或被分成有限的步骤，通过解决包含有限差分和附近点的数值的代数方程来逼近这些离散点的解的数值。
有限元方法finite differences method有限差分法将可能是非线性的常微分方程（ODE）或偏微分方程（PDE）转换成可以用矩阵代数技术解决的线性方程系统。现代计算机可以有效地进行这些线性代数计算，再加上其相对容易实现，使得FDM在现代数值分析中得到了广泛的应用。今天，FDM与有限元方法一样，是数值解决PDE的最常用方法之一。
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数学代写|有限元方法作业代写finite differences method代考|Background
One of the most important things engineers and scientists do is to model physical phenomena. Virtually every phenomenon in nature-whether aerospace, biological, chemical, geological, or mechanical – can be described, with the aid of the laws and axioms of physics or other fields, in terms of algebraic, differential, and/or integral equations relating various quantities that describe the phenomenon. Determining the stress distribution in a pressure vessel with oddly shaped holes and stiffeners and subjected to mechanical, thermal, and/or aerodynamic loads; finding the concentration of pollutants in lakes or in the atmosphere; and simulating weather in an attempt to understand and predict the formation of thunderstorms, tsunamis, and tornadoes are a few examples of many important practical problems that engineers deal with.
Analytical descriptions of physical or physiological processes in terms of pertinent variables are termed mathematical models. Mathematical models of a process are developed using assumptions concerning how the process works and using appropriate axioms or laws governing the process, and they are often characterized by very complex set of algebraic, differential, and/or integral equations posed on geometrically complicated domains.
Consequently, the processes to be studied, until the advent of electronic computation, were drastically simplified so that their mathematical models can be evaluated analytically. Over the last three decades, however, computers have made it possible, with the help of suitable mathematical models and numerical methods, to analyze many practical problems of engineering. The use of a numerical method and a computer to evaluate the mathematical model of a process and estimate its characteristics is called a numerical simulation. There now exists a new and growing body of knowledge connected with the development of mathematical models and use of numerical simulations of physical systems, and it is known as computational mechanics.
数学代写|有限元方法作业代写finite differences method代考|Mathematical Model Development
A mathematical model can be broadly defined as a set of equations that expresses the essential features of a physical system in terms of variables that describe the system. The mathematical models of physical phenomena are often based on fundamental scientific laws of physics such as the principle of conservation of mass, the principles of balance of linear and angular momentum, and the principle of balance of energy [2, 3]. The equations resulting from these principles are supplemented by equations that describe the constitutive behavior and by boundary and/or initial conditions. Next, we consider three simple examples drawn from dynamics, heat transfer, and solid mechanics to illustrate how mathematical models of physical problems are formulated. All mathematical models are not the exact representation of the physics; they are just models.
Example 1.2.1
Problem statement (Planar motion of a pendulum): A simple pendulum (such as the one used in a clock) consists of a bob of mass $m(\mathrm{~kg})$ attached to one end of a rod of length $\ell(\mathrm{m})$ with the other end pivoted to a fixed point O, as shown in Fig. 1.2.1(a). Make necessary simplifying assumptions to derive the governing equation for the simplest linear motion of the pendulum. Also, determine the analytical solution of the resulting equation for the case in which the initial conditions on the angular displacement $\theta$ and its derivative are specified.
有限元方法代写
数学代写|有限元方法作业代写finite differences method代考|Background
工程师和科学家所做的最重要的事情之一是模拟物理现象。事实上，自然界中的每一种现象——无论是航空航天、生物、化学、地质还是机械——都可以借助物理学或其他领域的定律和公理，用与描述该现象的各种量相关的代数、微分和/或积分方程来描述。确定具有奇怪形状孔和加强筋的压力容器承受机械、热和/或气动载荷时的应力分布;查明湖泊或大气中污染物的浓度;模拟天气，试图理解和预测雷暴、海啸和龙卷风的形成，这是工程师们处理的许多重要实际问题的几个例子。根据相关变量对物理或生理过程的分析性描述称为数学模型。一个过程的数学模型是使用过程如何工作的假设和使用适当的公理或控制过程的定律来建立的，它们通常以非常复杂的代数、微分和/或积分方程的集合为特征，这些方程是在几何复杂的域上提出的。因此，要研究的过程，直到电子计算的出现，都被大大简化，以便他们的数学模型可以分析地评估。然而，在过去的三十年里，计算机在合适的数学模型和数值方法的帮助下，使分析许多实际工程问题成为可能。使用数值方法和计算机来评估过程的数学模型并估计其特性称为数值模拟。
现在存在着一个新的和正在成长的知识体系，它与数学模型的发展和物理系统的数值模拟的使用有关，它被称为计算力学。
数学代写|有限元方法作业代写finite differences method代考|Mathematical Model Development
数学模型可以被广泛地定义为一组方程，这些方程用描述系统的变量来表达物理系统的基本特征。物理现象的数学模型往往基于基本的物理科学定律，如质量守恒原理、线动量和角动量平衡原理、能量平衡原理等[2,3]。由这些原理得出的方程由描述本构行为的方程以及边界和/或初始条件补充。接下来，我们考虑三个简单的例子，从动力学，传热和固体力学来说明如何制定物理问题的数学模型。并非所有的数学模型都能准确地表示物理现象;他们只是模特。
示例1.2.1
问题陈述(钟摆的平面运动):一个单摆(例如钟中的钟摆)由一个质量$m(\ mathm {~kg})$的摆组成，摆的一端系在一根长度$\ well (\ mathm {m})$的杆上，另一端转动到固定点O，如图1.2.1(a)所示。作必要的简化假设，以推导出钟摆最简单直线运动的控制方程。此外，确定角位移$\theta$及其导数的初始条件的情况下所得方程的解析解。
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