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   -> Volume 1, Issue 7


Preprint available
 
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Shann Wei-Chang, National Central University, Taiwan.
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PostPosted: Sun Oct 18, 1992 1:20 am    
Subject: Preprint available
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Preprint available

The following paper was done in May, 1991, with Prof. Jinchao Xu, when
I was a graduate student in Penn State. Our point of view was from
the finite element method. The key point is that the derivatives of
the one dimensional piecewise linear hierarchical basis is exactly the
Haar functions. Or, the lowest order of a family of Daubechies' wavelets
with compact support. We thus extend this idea to wavelets with higher
approximation power.

The article was accepted by Numerische Mathematik.

Jinchao Xu and Wei-Chang Shann
Galerkin-wavelets methods for two-point boundary value problems

Abstract. Anti-derivatives of wavelets are used for the numerical solution
of differential equations. Optimal error estimates are obtained in the
applications to two-point boundary value problems of second order.
The orthogonal property of the wavelets is used to construct efficient
iterative methods for the solution of the resultant linear algebraic systems.
Numerical examples are given.

Key words. Wavelets, finite element method, two-point boundary value problem,
conjugate gradient method, preconditioner, piecewise linear hierarchical basis.

A PostScript file with the text and graphics of this article can be obtained
from the anonymous ftp account in dongpo.math.ncu.edu.tw (140.115.25.3).
The file is pub/shann/wavelets/xu.ps. This is an ASCII file of length
about 422K. You can take the compressed version xu.ps.Z if you know how
to do it.

Printed copies can be requested from the address below.

Wei-Chang Shann, Associate Professor
Dept of Mathematics, National Central University, Chung-Li, Taiwan, R.O.C.
(03)425-6704 ext. 166 (work); (03)425-7379 (work.FAX)
shann@math.ncu.edu.tw
All times are GMT + 1 Hour
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