The One-Dimensional Stationary Heat Equation

Abstract

The homogeneous stationary one-dimensional heat equation with Dirichlet boundary conditions is solved analytically. It is then transformed into a system of inhomogeneous linear algebraic equations with tridiagonal matrix using the finite difference approximation of derivatives. It can, again, be solved analytically. The application of a heat source/drain transforms the heat equation into an inhomogeneous ordinary differential equation which can be transformed into a system of inhomogeneous linear algebraic equations with tridiagonal matrix. This system is solved numerically.