finite-difference approximation 中文意思是什麼

finite-difference approximation 解釋
有限差分近似式
  • finite : adj. 有限的；【語法】限定的；【數學】有窮的，有盡的。n. 〈the finite〉 有限（性）； 〈集合詞〉有限物。adv. -ly ,-ness n.
  • difference : n. 1. 差異，差別。2. 不和，爭論。3. 【數學】差，差額。4. 【邏輯學】特殊性。vt. 〈罕用語〉區別，使有差別。
  • approximation : n. 1. 接近；近似。2. 【數學】近似值。3. 概算，略計。
  1. ( 5 ) discuss some mathematical models of the pollutant transport problems in some local river flow fields. by integral transform method, the paper establishes the usual finite difference approximation scheme to solve the numerical solutions and gives examples for the computation of the approximating solutions, moreover, discusses one - dimensional characteristic finite difference method for a convection - diffusion equation under usual conditions

    （ 5 ）針對水域中污染物輸移問題的數學模型，通過積分變換法，得到了簡化模型在理想化條件下的近似精確解，同時給出數值算例，並且對非理想化條件下模型的特徵差分方法進行了討論。
  2. Author, secondly, starts from the approximate expandness of square root operator, perform mathematical calculations for finite difference operator in frequency - space domain, fourier finite difference operator in mixing domain ( frequency - space and frequency - wavenumber domain ) and general screen operator in mixing domain, compare and discuss their precision of their wavefield, adaptability for lateral velocity variations, computation efficiency and stability. thirdly, author, applies the steady variational reference slowness rytov approximation general screen wavefield extrapolation operator ( vrselrf ) in frequency - wavenumber domain, to the prestack and poststack forward modeling and depth migration

    第二，從平方根運算元的近似展開出發對頻率?空間域的有限差分運算元、混合域（頻率?空間域；頻率?波數域）的fourier有限差分運算元、混合域的廣義屏運算元進行了推導並對其波場描述精度、對橫向變速的適應性、計算效率和穩定性進行了比較與評述。
  3. This feature reflects the physical phenomenon of breaking of waves and development of shock waves. in the fields of fulid dynamics, ( 0. 2. 1 ) is an approximation of small visvosity phenomenon. if viscosity ( or the diffusion term, two derivatives ) are added to ( 0. 2. 1 ), it can be researched in the classical way which say that the solutions become very smooth immediately even for coarse inital data because of the diffusion of viscosity. a natural idea ( method of regularity ) is obtained as follows : solutions of the viscous convection - diffusion pr oblem approachs to the solutions of ( 0. 2. 1 ) when the viscosity goes to zeros. another method is numerical method such as difference methods, finite element method, spectrum method or finite volume method etc. numerical solutions which is constructed from the numerical scheme approximate to the solutions of the hyperbolic con - ervation laws ( 0. 2. 1 ) as the discretation parameter goes to zero. the aim of these two methods is to construct approximate solutions and then to conside the stability of approximate so - lutions ( i, e. the upper bound of approximate solutions in the suitable norms, especally for that independent of the approximate parameters ). using the compactness framework ( such as bv compactness, l1 compactness and compensated compactness etc ) and the fact that the truncation is small, the approximate function consquence approch to a function which is exactly the solutions of ( 0. 2. 1 ) in some sense of definiton

    當考慮粘性后，即在數學上反映為（ 0 . 1 . 1 ）中多了擴散項（二階導數項） ，即使很粗糙的初始數據，解在瞬間內變的很光滑，這由於流體的粘性擴散引起，這種對流-擴散問題可用古典的微分方程來研究。自然的想法就是當粘性趨于零時，帶粘性的對流-擴散問題的解在某意義下趨于無粘性問題（ 0 . 1 . 1 ）的解，這就是正則化方法。另一辦法從離散（數值）角度上研究僅有對流項的守恆律（ 0 . 1 . 1 ） ，如構造它的差分格式，甚至更一般的有限體積格式，有限元及譜方法等，從這些格式構造近似解（常表現為分片多項式）來逼近原守恆律的解。
  4. A stable finite difference approximation for vibration equation of beams

    梁振動方程的一個穩定的有限差分近似
  5. It is proposed on the basis of the analysis on newton method and the preconditioned conjugate gradient method ( pcg method ). numerical derivatives can be evaluated by symbolic differ - entiation ( sd ), finite difference approximation and automatic differelltiation ( ad ). ad has significant advantages over other two approaches

    自動微分是一種新的能精確而有效地計算導數的方法，它優越于傳統的微分方法，例如它比符號微分和差分方法的計算成本低，又比差分方法計算精確，自動微分在近幾年發展迅速，應用廣泛。
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