caa a22 4500 605496919 CHVBK 20210128100538.0 cr unu---uuuuu 210128e20150901xx s 000 0 eng 10.1007/s10543-014-0528-7 doi (NATIONALLICENCE)springer-10.1007/s10543-014-0528-7 Stability ordinates of Adams predictor-corrector methods [Elektronische Daten] [Michelle Ghrist, Bengt Fornberg, Jonah Reeger] How far the stability domain of a numerical method for approximating solutions to differential equations extends along the imaginary axis indicates how useful the method is for approximating solutions to wave equations; this maximum extent is termed the imaginary stability boundary, also known as the stability ordinate. It has previously been shown that exactly half of Adams-Bashforth (AB), Adams-Moulton (AM), and staggered Adams-Bashforth methods have nonzero stability ordinates. In this paper, we consider two categories of Adams predictor-corrector methods and prove that they follow a similar pattern. In particular, if $$p$$ p is the order of the method, AB $$p$$ p -AM $$p$$ p methods have nonzero stability ordinate only for $$p = 1, 2, \ 5, 6,\ 9, 10, \ldots $$ p = 1 , 2 , 5 , 6 , 9 , 10 , ... , and AB( $$p-$$ p - 1)-AM $$p$$ p methods have nonzero stability ordinates only for $$p = 3, 4, \ 7, 8, \ 11, 12, \ldots $$ p = 3 , 4 , 7 , 8 , 11 , 12 , ... . Springer Science+Business Media Dordrecht (outside the USA), 2014 Adams methods nationallicence Predictor-corrector nationallicence Imaginary stability boundary nationallicence Linear multistep methods nationallicence Finite difference methods nationallicence Stability region nationallicence Stability ordinate nationallicence Ghrist Michelle Department of Mathematical Sciences, United States Air Force Academy, 2354 Fairchild, Suite 6D2, 80840, USAF Academy, CO, USA aut Fornberg Bengt Department of Applied Mathematics, University of Colorado, Campus Box 526, 80309, Boulder, CO, USA aut Reeger Jonah Department of Mathematics and Statistics, Air Force Institute of Technology, 2950 Hobson Way, 45433, WPAFB, OH, USA aut BIT Numerical Mathematics Springer Netherlands 55/3(2015-09-01), 733-750 0006-3835 55:3<733 2015 55 10543 https://doi.org/10.1007/s10543-014-0528-7 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10543-014-0528-7 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Ghrist Michelle Department of Mathematical Sciences, United States Air Force Academy, 2354 Fairchild, Suite 6D2, 80840, USAF Academy, CO, USA aut NATIONALLICENCE 700 1- Fornberg Bengt Department of Applied Mathematics, University of Colorado, Campus Box 526, 80309, Boulder, CO, USA aut NATIONALLICENCE 700 1- Reeger Jonah Department of Mathematics and Statistics, Air Force Institute of Technology, 2950 Hobson Way, 45433, WPAFB, OH, USA aut NATIONALLICENCE 773 0- BIT Numerical Mathematics Springer Netherlands 55/3(2015-09-01), 733-750 0006-3835 55:3<733 2015 55 10543