Wasp: Wavelet Adaptive Solver for boundary value Problems

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 [t0,tf]
(2)       C0y(t0)+Cfy(tf) = d
where A and b are smooth functions, A(t), C0 and Cf being n by n matrices, b(t) and d vectors in Rn (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