**Description**

WASP is a small Matlab package designed for the numerical solution
of two-point linear boundary value problems, (LBVP), of the form

(1) dy/dt = A(t)y+b(t), t
in [t_{0},t_{f}]

(2) C_{0}y(t_{0})+C_{f}y(t_{f})
= d

where A and b are smooth functions, A(t), C_{0} and C_{f}
being n by n matrices, b(t) and d vectors in R^{n} (n is the dimension
of the problem). This kind of problem can be approximated by a linear system
using finite differences schemes [1]. The idea here
is to do so, but using moreover a grid refinement process so as to choose
adaptively the instants for the finite differences. Roughly speaking, thanks
to a wavelet analysis performed on the approximation of the solution to
(1)-(2) on a coarse grid (grid of resolution J), a new refined grid (of
resolution J+1) is computed by adding points whenever high wavelet coefficients
are detected. We refer to [3] for the details. The
package requires Matlab 4 or higher, together with the wavelet library
WaveLab [2], version v.701 or higher.

**References**

[1] U. M. Ascher, R. M. M. Mattheij
and R.~D. Russel, *Numerical solution of boundary value problems for
differential equations*, Prentice Hall, 1988.

[2] J. Buckheit, S. Chen, D. Donoho, I. Johnstone
and J. Scargle,
*WaveLab
reference manual*, tech. report, Stanford University, 1995.

[3] J. B. Caillau and J. Noailles, *Wavelets
for adaptive solution of boundary value problems*, Proceedings of
the 16th IMACS Conference,
M. Deville and R. Owens Eds., Lausanne, Switzerland, August 2000.

**Download**
WASP package for Matlab (4 or higher)

wasp-v1.zip (zip file)

wasp-v1.tar.gz (gziped archive)

WASP:
a Wavelet Adaptive Solver for boundary value Problems - Short Reference
Manual

Jean-Baptiste Caillau and Joseph Noailles

Technical Report RT/APO/01/1, ENSEEIHT-IRIT, January 2001.

Wavelets
for adaptive solution of boundary value problems

Jean-Baptiste Caillau and Joseph Noailles

16th IMACS World Congress 2000, pp. 1-6, ISBN 3-9522075-1-9, Lausanne,
Switzerland, August 2000.

Link to WaveLab
at Stanford.

caillau@n7.fr

Last modified: Fri January 5, 19:48:55 MET DST 2001