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   -> Volume 2, Issue 10

Preprint available:
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Author Message
Wei Cai, Department of Mathematics, University of North Carolina.

PostPosted: Fri Nov 29, 2002 3:32 pm    
Subject: Preprint available:
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Preprint available:

Preprint can be requested for the following paper:

"Adaptive Wavelet Collocation Methods for
Initial Value Boundary Problems of Nonlinear PDE's"

Authors: Wei Cai
Department of Mathematics,
University of North Carolina at Charlotte
Charlotte, NC 28223

JianZhong Wang
Department of Mathematics, Wuhan University
Wuhan, P.R. China


We have designed a cubic spline wavelet decomposition for the
Sobolev space $H^2_0(I)$ where $I$ is a bounded interval.
Based on a special ``point-wise orthogonality" of the wavelet
basis functions, a fast Discrete Wavelet Transform (DWT) is constructed.
This DWT transform will map discrete samples of a function to its
wavelet expansion coefficients in $O(Nlog{N})$ operations.
Using this transform, we propose a collocation method
for the initial value boundary problem of nonlinear PDE's.
Then, we test the efficiency of the DWT transform and
apply the collocation method to solve linear and nonlinear PDE's.

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