线性边界条件热传导方程求解

On the Solving of Heat Conduction Equation of Linear Boundary Conditions

热传导方程是工程中很重要的偏微分方程,工程上利用它描述某个区域内的温度如何随时间变化,这种方程常被称作扩散方程。研究热传导方程的解具有很重要的意义。本文主要介绍解一维线性初边值热方程的分离变量法及其pdepe数值解法。结合实例讲述了如何用pdepe函数编程求解热传导方程。

The heat conduction equation is an important partial differential equation in engineering, in which it is used to de-scribe how the temperature changes with time within a certain area, and such an equation is often called diffusion equation. It is of great significance to research the solving of the heat conduction equation. This paper mainly introduced the method of separation of variables for the solving of one-dimensional linear initial boundary value heat equation and the method of solving its pdepe numerical value. Combined with practical cases, this paper elab-orated how to use pdepe functional programming to solve heat e-quation.