SOLVING THE HEAT AND WAVE EQUATIONS WITH THE (FAST) DISCRETE FOURIER TRANSFORM

In this paper, we present in detail a little known application of the fast Discrete Fourier Transform (DFT), also known as FFT. Namely, we first examine the use of FFT in approximating polynomials with sines and cosines (also known as Fast Fourier Fit or FFF) and then derive and solve the heat and wave equations.