In this article we introduce a new mixed Lagrange-Hermite interpolating wavelet family on the interval, to deal with two types (Dirichlet and Neumann) of boundary conditions. As this construction is a slight modification of the interpolating wavelets on the interval of Donoho, it leads to fast decomposition, error estimates and norm equivalences. This new basis is then used in adaptive wavelet collocation schemes for the solution of one dimensional fourth order problems. Numerical tests conducted on the 1D Euler-Bernoulli beam problem, show the efficiency of the method.
A new construction of boundary interpolating wavelets for fourth order problems
S Bertoluzza;
2017
Abstract
In this article we introduce a new mixed Lagrange-Hermite interpolating wavelet family on the interval, to deal with two types (Dirichlet and Neumann) of boundary conditions. As this construction is a slight modification of the interpolating wavelets on the interval of Donoho, it leads to fast decomposition, error estimates and norm equivalences. This new basis is then used in adaptive wavelet collocation schemes for the solution of one dimensional fourth order problems. Numerical tests conducted on the 1D Euler-Bernoulli beam problem, show the efficiency of the method.File in questo prodotto:
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Descrizione: A new construction of boundary interpolating wavelets for fourth order problems
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