V2EX finite-difference

Finite-Difference

释义 Definition

有限差分(法):一种用离散网格点上的差值来近似导数的数值方法,常用于求解微分方程(尤其是偏微分方程)与数值模拟(如热传导、流体、波动)。也常作形容词:finite-difference scheme/method(有限差分格式/方法)。

发音 Pronunciation

/fanat df()rns/

例句 Examples

The finite-difference method approximates derivatives using nearby grid points.
有限差分法通过相邻网格点来近似导数。

To model heat diffusion, we implemented a finite-difference scheme with stable time stepping and boundary conditions.
为模拟热扩散,我们实现了带稳定时间步进与边界条件的有限差分格式。

词源 Etymology

finite(有限的)+ difference(差、差分)。该术语源于数值分析与计算数学的表达习惯:把连续函数在离散点上的变化用“差分”表示,从而用有限的、可计算的差值去逼近连续的微分运算。

相关词 Related Words

文献与著作 Notable Works

  • Finite Difference Methods for Ordinary and Partial Differential Equations(Randall J. LeVeque)
  • Numerical Recipes: The Art of Scientific Computing(Press et al.)
  • Computational Fluid Dynamics: The Basics with Applications(John D. Anderson, Jr.)
  • Partial Differential Equations for Scientists and Engineers(Stanley J. Farlow)
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