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Spline-wavelets techniques for heat propagation. (English) Zbl 1049.65104
The Fourier solution of a mixed parabolic heat problem is considered and compared with the wavelet solution and 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. An estimate of the numerical approximation error is given.
MSC:
65M70Spectral, collocation and related methods (IVP of PDE)
65T60Wavelets (numerical methods)
65M15Error bounds (IVP of PDE)
35K05Heat equation
35K20Second order parabolic equations, initial boundary value problems