翻訳と辞書
Words near each other
・ Compact convergence
・ Compact dimension
・ Compact disc
・ Compact Disc + Extended Graphics
・ Compact Disc and DVD copy protection
・ Compact Disc bronzing
・ Compact Disc Digital Audio
・ Compact Disc File System
・ Compact Disc manufacturing
・ Compact Disc subcode
・ Compact Disco
・ Compact Disk Dummies
・ Compact element
・ Compact excavator
・ Compact executive car
Compact finite difference
・ Compact fluorescent lamp
・ Compact Forest Proposal
・ Compact government
・ Compact group
・ Compact intracloud discharge
・ Compact Kinetic Energy Missile
・ Compact Lie algebra
・ Compact Linear Collider
・ Compact linear Fresnel reflector
・ Compact Macintosh
・ Compact Model Coalition
・ Compact MPV
・ Compact Muon Solenoid
・ Compact of 1802


Dictionary Lists
翻訳と辞書 辞書検索 [ 開発暫定版 ]
スポンサード リンク

Compact finite difference : ウィキペディア英語版
Compact finite difference

The compact finite difference (CTFD) formulation, or Hermitian formulation, is a numerical method to solve the compressible Navier–Stokes equation. This method is both accurate and numerically very stable (especially for high-order derivatives).
The expression for partial derivatives is developed and expressed mainly on dependent variables. An approach to increase accuracy of the estimates of the derivatives, in particular a problem involving shorter length scales or equivalently high frequencies, is to include the influence of the neighboring points in the calculations. This approach is analogous to the solution of a partial differential equation by an Implicit scheme to an explicit scheme. The resulting approximation is called a compact finite difference (CTFD) formulation or a Hermitian formulation.
Forward difference formulae and backward difference formulae are first order accurate, and central difference formula are second order accurate; compact finite difference formulae provide a more accurate method to solve equations.
==Compact finite difference formulation==

===First order derivatives===
Consider a three-point Hermitian formula involving the first derivative:
: H_=\sum_^\ell (a_m f_ + b_mf'_) = 0. \qquad (1)
Substituting the Taylor series expansion of the terms fi+1 and fi-1 results in:
In the above expression, only the first few terms are to be considered zero, and the rest of the higher order terms will be considered as the (error (numerical integration)|truncation error )] (TE). To obtain a third-order scheme, the coefficients of ''f''''i'' , ''f'''''i'', ''f''''''i'' , ''f''''i'' will be zero. If it is a fourth-order scheme, the coefficient of f’’’’i will also be zero.
From the above equations, one can solve for a1 , a0 , a-1 and b0 in the form of b1 and b-1



The Truncation error will be:



Substituting (4) in the above equation results in:



The standard compact finite difference formula for first order derivatives of f(x) has a 3 point formulation

() (+ 4f’i + f’i+1 ) = -fi-1 + fi+1

where f’i = df(xi)/dx

Similarly, for a fifth point formulation, take m=2 in the beginning.

One-parameter family of compact finite difference schemes for first order derivatives Scheme




抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
ウィキペディアで「Compact finite difference」の詳細全文を読む



スポンサード リンク
翻訳と辞書 : 翻訳のためのインターネットリソース

Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.