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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Notes
- 1.
We note that Eq. (9.20) can also be solved with the help of Fourier transforms, see Appendix D.
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Stickler, B.A., Schachinger, E. (2016). The One-Dimensional Stationary Heat Equation. In: Basic Concepts in Computational Physics. Springer, Cham. https://doi.org/10.1007/978-3-319-27265-8_9
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DOI: https://doi.org/10.1007/978-3-319-27265-8_9
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