Wavelets for adaptive solution of boundary value problems

An adaptive discretization technique for boundary value problems is proposed; the mesh computation essentially involves a wavelet analysis. The process is used to enhance usual methods such as finite differences for linear BVPs or multiple shooting for nonlinear ones. Comparisons with classical non-adaptive Chebyshev spectral or peusospectral methods are drawn, in particular in the case of a BVP issuing from nonlinear optimal control.