TIME-DOMAIN SIMULATION OF FUNCTIONS AND DYNAMICAL SYSTEMS OF BESSEL TYPE

∗ Work supported by the CONSONNES project, ANR-05-BLAN-0097-01. Two methods are investigated for the time-domain si-mulation of functions and dynamical systems of Bessel type, involved in wave propagation (see e.g. [1], [8], [2]). Both are based on complex analysis and lead to finite-dimensional approximations. The first method relies on optimized parametric contours and provides asymptotic convergence rates. The second is based on cuts and in-tegral representations, whose approximations prove effi-cient, even at low orders, using ad hoc frequency criteria. 1 Model under study For ℜe(s)> −ε, let Ĵε(s) = [(s + ε)2 + 1]−1/2 be the Laplace transform of Jε(t) = e−εt J0(t) for t ≥ 0 (cf. [3]). The general formula can be derived: Jε(t) =