V2EX integro-differential equation

Integro-differential Equation

Definition / 释义

积分-微分方程:一种同时包含未知函数的导数项积分项的方程,常用于描述带有“记忆效应”或“非局部相互作用”的系统。(也可能有不同类型,如 Volterra 型、Fredholm 型等。)

Pronunciation / 发音

/n.t.ro df.rn.l kwe.n/

Examples / 例句

The model leads to an integro-differential equation.
这个模型会导出一个积分-微分方程。

To capture the system’s memory effect, we solve an integro-differential equation with a convolution integral term.
为刻画系统的记忆效应,我们求解一个包含卷积积分项的积分-微分方程。

Etymology / 词源

integro- 来自 integral(积分),源于拉丁语 integer(“完整的”),引申为“整体求和/累积”的数学概念;differential(微分的)来自拉丁语 differentia(差异),对应“变化率/差分”;两者合成用来指“把积分与微分运算同时纳入同一方程”的结构。该术语多见于数学物、工程与概率过程等领域的英文文献中。

Related Words / 相关词

Literary Works / 文学与著作示例

  • Methods of Mathematical Physics(Courant & Hilbert)在数学物理建模中讨论包含积分项与微分项的方程形式
  • Theoretical Physics(Landau & Lifshitz, 多卷)在输运、连续介质与统计相关问题中常出现此类方程
  • Mathematical Methods for Physicists(Arfken, Weber & Harris)作为物理问题的常见方程类型在相关章节出现
  • Integral Equations(Tricomi)讨论积分方程及其与微分形式的联系,涉及积分-微分混合问题
  • Stochastic Processes(Gardiner)在含记忆核/非马尔可夫效应的模型推导中常见此类方程表述
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