V2EX boundary value problem

Boundary Value Problem

释义 / Definition

边值问题:数学中指一种微分方程(常见于常微分方程与偏微分方程)的问题类型,其解不仅要满足方程本身,还必须满足在定义域边界(或若干指定点/边界面)给定的条件(边界条件)。

发音 / Pronunciation (IPA)

/band()ri vlju prblm/

例句 / Examples

A boundary value problem needs boundary conditions to be solved.
边值问题需要边界条件才能求解。

We modeled the heat flow in the metal rod as a boundary value problem, specifying the temperature at both ends.
我们把金属棒中的热传导建模为一个边值问题,并给定两端的温度作为边界条件。

词源 / Etymology

该短语由 boundary(边界)+ value(取值/数值)+ problem(问题) 组合而成,字面意思是“边界取值所规定的问题”。它在数学物理与微分方程理论中形成专门术语,用来区别于以初始时刻条件为主的 initial value problem(初值问题)

相关词 / Related Words

文学与名著用例 / Notable Works

  • Methods of Mathematical Physics Richard Courant & David Hilbert(讨论边值问题在数学物理中的核心地位)
  • Partial Differential Equations Lawrence C. Evans(大量出现并系统讲解边值问题框架)
  • Mathematical Methods for Physicists Arfken, Weber & Harris(在物理建模中频繁涉及边值问题)
  • Equations of Mathematical Physics V. S. Vladimirov(以边值问题组织多个经典方程的求解思路)
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