Stability ordinates of Adams predictor-corrector methods
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| 008 | 210128e20150901xx s 000 0 eng | ||
| 024 | 7 | 0 | |a 10.1007/s10543-014-0528-7 |2 doi |
| 035 | |a (NATIONALLICENCE)springer-10.1007/s10543-014-0528-7 | ||
| 245 | 0 | 0 | |a Stability ordinates of Adams predictor-corrector methods |h [Elektronische Daten] |c [Michelle Ghrist, Bengt Fornberg, Jonah Reeger] |
| 520 | 3 | |a 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 , ... . | |
| 540 | |a Springer Science+Business Media Dordrecht (outside the USA), 2014 | ||
| 690 | 7 | |a Adams methods |2 nationallicence | |
| 690 | 7 | |a Predictor-corrector |2 nationallicence | |
| 690 | 7 | |a Imaginary stability boundary |2 nationallicence | |
| 690 | 7 | |a Linear multistep methods |2 nationallicence | |
| 690 | 7 | |a Finite difference methods |2 nationallicence | |
| 690 | 7 | |a Stability region |2 nationallicence | |
| 690 | 7 | |a Stability ordinate |2 nationallicence | |
| 700 | 1 | |a Ghrist |D Michelle |u Department of Mathematical Sciences, United States Air Force Academy, 2354 Fairchild, Suite 6D2, 80840, USAF Academy, CO, USA |4 aut | |
| 700 | 1 | |a Fornberg |D Bengt |u Department of Applied Mathematics, University of Colorado, Campus Box 526, 80309, Boulder, CO, USA |4 aut | |
| 700 | 1 | |a Reeger |D Jonah |u Department of Mathematics and Statistics, Air Force Institute of Technology, 2950 Hobson Way, 45433, WPAFB, OH, USA |4 aut | |
| 773 | 0 | |t BIT Numerical Mathematics |d Springer Netherlands |g 55/3(2015-09-01), 733-750 |x 0006-3835 |q 55:3<733 |1 2015 |2 55 |o 10543 | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/s10543-014-0528-7 |q text/html |z Onlinezugriff via DOI |
| 898 | |a BK010053 |b XK010053 |c XK010000 | ||
| 900 | 7 | |a Metadata rights reserved |b Springer special CC-BY-NC licence |2 nationallicence | |
| 908 | |D 1 |a research-article |2 jats | ||
| 949 | |B NATIONALLICENCE |F NATIONALLICENCE |b NL-springer | ||
| 950 | |B NATIONALLICENCE |P 856 |E 40 |u https://doi.org/10.1007/s10543-014-0528-7 |q text/html |z Onlinezugriff via DOI | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Ghrist |D Michelle |u Department of Mathematical Sciences, United States Air Force Academy, 2354 Fairchild, Suite 6D2, 80840, USAF Academy, CO, USA |4 aut | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Fornberg |D Bengt |u Department of Applied Mathematics, University of Colorado, Campus Box 526, 80309, Boulder, CO, USA |4 aut | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Reeger |D Jonah |u Department of Mathematics and Statistics, Air Force Institute of Technology, 2950 Hobson Way, 45433, WPAFB, OH, USA |4 aut | ||
| 950 | |B NATIONALLICENCE |P 773 |E 0- |t BIT Numerical Mathematics |d Springer Netherlands |g 55/3(2015-09-01), 733-750 |x 0006-3835 |q 55:3<733 |1 2015 |2 55 |o 10543 | ||