Wavelets for Adaptive Solution of Boundary Value Problems
Jean‐Baptiste Caillau, Joseph Noailles · 2000
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 nite dierences 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. Key words: boundary value problems, adaptive discretization, wavelet analysis, multiple shooting and nite dierence methods, nonlinear optimal control. AMS subject classications: 65L10, 65L50, 42C99, 49M05. 1 Introduction Among the classical methods for the numerical solution of boundary value problems with ordinary dierential equations, we can distinguish several parametrization levels of the underlying time discretizations: while spectral or pseudospectral techniques [1, 8] are only parametrized by the number of points used for the quadratures, nit...