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有限差分法   finite difference method   微分方程和积分微分方程数值解的方法。基本思想是把连续的定解区域用有限个离散点构成的网格来代替, 这些离散点称作网格的节点;把连续定解区域上的连续变量的函数用在网格上定义的离散变量函数来近似;把原方程和定解条件中的微商用差商来近似, 积分用积分和来近似,于是原微分方程和定解条件就近似地代之以代数方程组,即有限差分方程组 , 解此方程组就可以得到原问题在离散点上的近似解。然后再利用插值方法便可以从离散解得到定解问题在整个区域上的近似解。   有限差分法的主要内容包括:如何根据问题的特点将定解区域作网格剖分;如何把原微分方程离散化为差分方程组以及如何解此代数方程组。此外为了保证计算过程的可行和计算结果的正确,还需从理论上分析差分方程组的性态,包括解的唯一性、存在性和差分格式的相容性、收敛性和稳定性。对于一个微分方程建立的各种差分格式,为了有实用意义,一个基本要求是它们能够任意逼近微分方程,这就是相容性要求。另外,一个差分格式是否有用,最终要看差分方程的精确解能否任意逼近微分方程的解,这就是收敛性的概念。此外,还有一个重要的概念必须考虑,即差分格式的稳定性。因为差分格式的计算过程是逐层推进的,在计算第n+1层的近似值时要用到第n层的近似值 ,直到与初始值有关。前面各层若有舍入误差,必然影响到后面各层的值,如果误差的影响越来越大,以致差分格式的精确解的面貌完全被掩盖,这种格式是不稳定的,相反如果误差的传播是可以控制的,就认为格式是稳定的。只有在这种情形,差分格式在实际计算中的近似解才可能任意逼近差分方程的精确解。关于差分格式的构造一般有以下3种方法。最常用的方法是数值微分法,比如用差商代替微商等。另一方法叫积分插值法,因为在实际问题中得出的微分方程常常反映物理上的某种守恒原理,一般可以通过积分形式来表示。此外还可以用待定系数法构造一些精度较高的差分格式。
"有限差分法"的最佳翻译为"finite difference",相关的英文翻译自动加入检索

有限差分解决温度的对流扩散问题 finite difference method to solve the problem of temperature(heat)-zhulin123456分享

有限差分解决温度的对流扩散问题 finite difference method to solve the problem of temperature(heat)-zhulin123456分享
finite difference method to solve the problem of temperature(heat) 有限差分解决温度的对流扩散问题 2009年05月22日 zhulin123456  

temperature analysis using finite difference method

temperature analysis using finite difference method
% Study of heat transfer and temperature of a 1x1 metal plate %heat is dissipated through the left right and bottom sides and temp at infinity is t % finite difference method, heat, temperature, Chemistry, Physics
Fast Automatic Differentiation in C++

Fast Automatic Differentiation in C++

有限差分法定温度分析程序源代码免费下载-temperature analysis using finite difference method-Free Source Code

有限差分法定温度分析程序源代码免费下载-temperature analysis using finite difference method-Free Source Code
有限差分法定温度分析程序 temperature analysis using finite difference method 2008年10月03日 Matlab R14 这个程序用有限差分法分析,当一个从一边受热的方型物体放置空气中,之后,

Finite difference weights

Finds finite difference (or interpolation) weights for an arbitrary set of nodes in one dimension....formula due to Fornberg (A Practical Guide to Pseudospectral Methods, Cambridge University Press).

Essentials of Computational Physics. Part 1: An introduction to finite-difference methods

Designed for graduate students in physics and engineering, this package covers a variety of finite-differenceCompanion software package. Physics. Numerical methods, PDE, physics, engineering, finite-difference, heat

Finite Difference Weights

Computes the finite difference for a uniform grid. Differential Equations. Finite, Difference, Approximation, Numerical, Differential, Equations

One Dimensional Finite Difference Time Domain

.. General Communications. Finite Difference Time Domain, FDTD, 1D, cartesian, test,...k_obs) % % This function performs one-dimensional (Cartesian) finite-difference time-domain % simulations.

三维有限光束传播法 Finite Differences Beam Propagation Method in 3-D-两会分享

三维有限光束传播法 Finite Differences Beam Propagation Method in 3-D-两会分享
Finite Differences Beam Propagation Method in 3-D 三维有限光束传播法 2009年03月20日 两会  热心分享 MATLAB 6.5 该程序仿真了在三维空间中高斯脉冲的传播。

Finite Difference Beam Propagation Method

Finite Difference Beam Propagation Method
Simulation of a gaussian pulse propagated in free space through 1000 um, using finite differences. Just run the script and you'll get a surface which is made up of the pulse propagated at 1 um steps.

一维时域有限差分的程序 - One Dimensional Finite Difference Time Domain

计算一维时域有限差分的程序。 A function to calculate 1D FDTD, and two test scripts计算一维时域有限差分的程序。 A function to calculate 1D FDTD, and two test scripts

CaspLab - Comet Assay Software Project

CASP - Comet Assay Software Project is a cross-platform image analysis software to measure level of DNA damage in SCGE (Single Cell Gel Electrophoresis) method called also comet assay method.

LMFsolve.m: Levenberg-Marquardt-Fletcher algorithm for nonlinear least squares problems

LMFsolve.m: Levenberg-Marquardt-Fletcher algorithm for nonlinear least squares problems
The standard Levenberg- Marquardt algorithm was modified by Fletcher ... default values of options are used.... internal function for finite difference approximation of the matrix is used.

An Example of Markov Chain and multinominal option pricing

As a coursework, we are required to price a double barriers knock-in binary put option. We used finite difference method in 24 ways and We used finite difference method in 24 ways and multinomial lattice in 12 ways.

Waveguide Mode Solver

Waveguide Mode Solver
optical waveguides using the finite difference method. Features: 1. Includes vector, semivector, and scalar versions.

LMFnlsq - Solution of nonlinear least squares

LMFnlsq - Solution of nonlinear least squares
modification of Levenberg-Marquardt method Optimization. Levenberg,... The standard Levenberg- Marquardt algorithm was modified by Fletcher ... default structure items are used.

Capind the RLGC Calculator

Capind is a program for calculating RLGC matrix of multi-conductor transmission lines of arbitrary shape and Capind is based on finite difference method and features easy-to-use input files and optional graphical

adicell

Finite difference modeling of human head electromagnetics using alternating direction implicit (ADI) method ported to the IBM Cell Broadband Engine.

Numerical Laplace Transforms and Inverse Transforms in C#

Numerical Laplace Transforms and Inverse Transforms in C#
a C# implementation of the Stehfest algorithm for Laplace transform ... the diffusivity equation used for radial flow of a single ... but requires the use of finite difference approximations or other

Fast Automatic Differentiation in C++

Fast Automatic Differentiation in C++
the well-known symbolic and finite difference approaches....like to outline the benefits of this approach and describe my own ...and how the derivatives of a function can be used.

FDTD Studio

DEVELOPMENT OF AN INTEGRATED INTERFACE FOR THE PROJECT AND ANALYSIS OF ANTENNAS USING THE FINITE DIFFERENCE TIME DOMAIN METHODTHE PROJECT AND ANALYSIS OF ANTENNAS USING THE FINITE DIFFERENCE TIME DOMAIN METHOD (FDTD)
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