Mixed Boundary-Value Problem for the One-Dimensional Heat Equation

This Demonstration determines solutions to the mixed boundary-value problem for the one-dimensional heat equation. This pertains to the conduction of heat in a bar in which the ends are kept at fixed temperatures (0º in this case), with a specified initial temperature distribution, .


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We approximate by the first five terms of its Fourier sine series representation, that is, we take ; then it can be shown that the solution is .
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