Order Stars

Abstract

Order stars, discovered by searching for a better understanding of the stability properties of the Padé approximations to e ^z (Wanner, Hairer & Nørsett 1978), offered nice and unexpected access to many other results: the “second barrier” of Dahlquist, the Daniel & Moore conjecture, highest possible order with real poles, comparison of stability domains (Jeltsch & Nevanlinna 1981, 1982), order bounds for hyperbolic or parabolic difference schemes (e.g., Iserles & Strang 1983, Iserles & Williamson 1983, Jeltsch 1988).