格林公式在微分方程中的应用
Application of Green’s Formula in Differential Equations
摘要: 本文研究了常见的非齐次常微分方程和偏微分方程的格林函数解法。本文首先根据特殊的偏微分方程的物理意义分别求出了它们的格林函数，从而得到了它们的解。对于物理意义不明显的非齐次常微分方程，本文从最简单的一阶线性方程开始讨论，进一步地，推导出了高阶线性方程的格林函数。
Abstract: This paper investigates the Green’s function solution of common non-homogeneous ordinary dif-ferential equations and partial differential equations. We first obtain Green’s functions according to the physical meanings of special partial differential equations. Then we yield their solutions. Considering non-homogeneous ordinary differential equations with insignificant physical meanings, this paper begins with the simplest first-order linear equations. Furthermore, the Green’s function of higher-order linear equations is derived.
文章引用：周悦, 熊艳琴. 格林公式在微分方程中的应用[J]. 应用数学进展, 2018, 7(9): 1174-1190. https://doi.org/10.12677/AAM.2018.79137

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