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.
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