Spline-Wavelet Solutions for Diffusion Equation

Carlo Cattani; E. Laserra; M. Pecoraro

doi:10.1615/InterJFluidMechRes.v29.i6.20

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Home > Journals > International Journal of Fluid Mechanics Research > Volume 29, 2002 Issue 6 > Spline-Wavelet Solutions for Diffusion Equation

ISSN Print: 1064-2277
ISSN Online: 2152-5102

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International Journal of Fluid Mechanics Research

DOI: 10.1615/InterJFluidMechRes.v29.i6.20
8 pages

Spline-Wavelet Solutions for Diffusion Equation

Carlo Cattani
Dipartimento di Matematica "G. Castelnuovo", Univ. di Roma "La Sapienza'' P. Ie A. Moro 5,1-00185 Roma ; and DiFarma, University of Salerno Via Ponte Don Melillo, 84084 Fisciano (SA), Italy

E. Laserra
Dipartimento di Matematica e Informatica, Univ. di Salerno, Via S.Allende, 1-84121 Baronissi (SA), Italy

M. Pecoraro
Universita di Salerno, Via S.AUende, 1-84081 Baronissi (SA), Italy

ABSTRACT

In this paper, the Fourier solution of a mixed parabolic diffusion problem is considered and compared with the wavelet solution and with a cardinal cubic spline solution. The wavelet solution is obtained using the discrete Haar transform and the Haar wavelets are regularized by natural splines. The cubic spline solution is obtained defining a fast Spline Haar transform via matrix product.