Spline-wavelets Techniques for Heat Propagation

In this paper the Fourier solution of a mixed parabolic heat problem is considered and compared (a) with the wavelet solution and (b) with a cardinal cubic spline series expansion. The wavelet solution is obtained by using the fast Haar transform and the Haar wavelets regularized by natural splines. The cubic spline solution is obtained by defining a fast Spline Haar transform via a matrix product.