caa a22 4500 46582112X CHVBK 20180323112136.0 cr unu---uuuuu 170327e19900901xx s 000 0 eng 10.1007/BF01931665 doi (NATIONALLICENCE)springer-10.1007/BF01931665 van der Marel Roeland Department of Mathematics and Computer Science, University of Leiden, Niels Bohrweg 1, 2333 CA, Leiden, The Netherlands aut Stability radius of polynomials occurring in the numerical solution of initial value problems [Elektronische Daten] [Roeland van der Marel] This paper deals with polynomial approximationsφ(x) to the exponential function exp(x) related to numerical procedures for solving initial value problems. Motivated by stability requirements, we present a numerical study of the largest diskD(ρ)={z ∈ C: |z+ρ|≤ρ} that is contained in the stability regionS(φ)={z ∈C: |φ(z)|≤1}. The radius of this largest disk is denoted byr(φ), the stability radius. On the basis of our numerical study, several conjectures are made concerningr m,p=sup {r(φ):φ εΠ m,p}. HereΠ m, p (1≤p≤m; p, m integers) is the class of all polynomialsφ(x) with real coefficients and degree ≤m for whichφ(x)=exp(x)+O(x p+1) (forx → 0). BIT Foundations, 1990 Numerical analysis nationallicence Initial Value Problems nationallicence Explicit Methods nationallicence Stability nationallicence Stability Region nationallicence Circle Condition nationallicence BIT Numerical Mathematics Kluwer Academic Publishers 30/3(1990-09-01), 516-528 0006-3835 30:3<516 1990 30 10543 https://doi.org/10.1007/BF01931665 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF01931665 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- van der Marel Roeland Department of Mathematics and Computer Science, University of Leiden, Niels Bohrweg 1, 2333 CA, Leiden, The Netherlands aut NATIONALLICENCE 773 0- BIT Numerical Mathematics Kluwer Academic Publishers 30/3(1990-09-01), 516-528 0006-3835 30:3<516 1990 30 10543 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer