利用Python求解拉普拉斯椭圆方程中热传导问题

Using Python to Solve the Heat Conduction Problem in Laplace Elliptic Equation

拉普拉斯方程(Laplace’s Equation)是最简单的二阶偏微分方程之一,也是最简单的椭圆形偏微分方程。它在数学、物理学中有举足轻重的地位,因为它能够描述电势能和热传导问题。在热传导中,它被称为稳态热方程或热传导方程。文中将使用数值求解代替积分求解,在给定边界温度的情况下,用Python并通过数值求解来解该方程,以得到二维平面内每个点的稳定温度。给定边界温度后,我们可以在解决热传导问题时,直观地得出拉普拉斯方程的解。

Laplace's equation:(Laplace’s equation),It is one of the simplest second-order partial differential equations and also the simplest elliptical partial differential equation.It plays an important role in mathematics and physics because it can describe electric potential energy and heat conduction problems.In heat conduction,it is referred to as the steady-state heat equation or heat conduction equation.In this article,numerical solution will be used instead of integral solution.Given the boundary temperature,the equation will be solved using Python programming language and numerical solution to obtain the stable temperature of each point in the two-dimensional plane.Given the boundary temperature,we can intuitively obtain the solution of Laplace's equation when solving the heat conduction problem.