Time-domain Simulation of Functions and Dynamical Systems of Bessel Type

Two methods are investigated for the time-domain simulation 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 finitedimensional approximations. The first method relies on optimized parametric contours and provides asymptotic convergence rates. The second is based on cuts and integral representations, whose approximations prove efficient, 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: