Heat equation

This shows the time evolution of a solution for the heat equation ut = βuxx given an initial condition, and subject to the boundary conditions of the left and right endpoints being fixed at zero.

Click and drag to adjust the current temperature at different points. The light grey lines are different terms of the Fourier series at the current moment — the linear combination of these gives the black line.

Try creating "high-frequency" temperature curves and see how much quicker they decay compared to the remaining "low-frequency" components.

Try tracing out different sine waves to see how the Fourier transform identifies them.

©2016 Kyle Miller