The stability problem for linear multistep methods: Old and new results
作者： L. Aceto , D. Trigiante
DOI: 10.1016/J.CAM.2006.10.052
关键词: Applied mathematics 、 Runge–Kutta methods 、 Stability (learning theory) 、 Numerical stability 、 Linear stability 、 Calculus 、 Order (group theory) 、 Mathematics 、 Numerical analysis 、 Differential equation 、 Linear multistep method
摘要: The paper reviews results on rigorous proofs for stability properties of classes linear multistep methods (LMMs) used either as IVMs or BVMs. considered are not only the well-known classical ones (BDF, Adams, ...) along with their BVM correspondent, but also those which were unstable IVMs, stable Among latter we find two deserve attention because peculiarity: TOMs (top order methods) have highest allowed to a LMM and Bs-LMMs property carry each method its natural continuous extension.
harvard.edu
elsevier.com
core.ac.uk 
sci-hub.se 参考文章(15)
Germund Dahlquist, Positive Functions and some Applications to Stability Questions for Numerical Methods Recent Advances in Numerical Analysis#R##N#Proceedings of a Symposium Conducted by the Mathematics Research Center, the University of Wisconsin–Madison, May 22–24, 1978. pp. 1- 29 ,(1978) , 10.1016/B978-0-12-208360-0.50006-1
D. Trigiante, L Brugnano, Solving differential problems by multistep initial and boundary value methods Gordon & Breach. ,(1998)
John Denholm Lambert, Computational Methods in Ordinary Differential Equations ,(1973)
V Lakshmikantham, Donato Trigiante, Theory Of Difference Equations Numerical Methods And Applications ,(2002)
Lidia Aceto, Donato Trigiante, On the A-stable methods in the GBDF class Nonlinear Analysis: Real World Applications. ,vol. 3, pp. 9- 23 ,(2002) , 10.1016/S1468-1218(01)00009-8
Carl de Boor, Gene H. Golub, Recent Advances in Numerical Analysis. Mathematics of Computation. ,vol. 38, pp. 654- ,(1982) , 10.2307/2007307
Francesca Mazzia, Alessandra Sestini, Donato Trigiante, B-Spline Linear Multistep Methods and their Continuous Extensions SIAM Journal on Numerical Analysis. ,vol. 44, pp. 1954- 1973 ,(2006) , 10.1137/040614748
Peter Henrici, Henry C. Thacher, Applied and Computational Complex Analysis ,(1974)
Lidia Aceto, Donato Trigiante, The Matrices of Pascal and Other Greats American Mathematical Monthly. ,vol. 108, pp. 232- 245 ,(2001) , 10.1080/00029890.2001.11919745
Donato Trigiante, Albert Stadler, Where Are the Zeros?: 10995 American Mathematical Monthly. ,vol. 111, pp. 917- ,(2004) , 10.2307/4145110