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)
Description