TY - JOUR
T1 - Comparison of boundedness and monotonicity properties of one-leg and linear multistep methods
AU - Mozartova, A.
AU - Savostianov, I.
AU - Hundsdorfer, W.
N1 - KAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): FIC/2010/05
Acknowledgements: The work of A. Mozartova has been supported by a grant from the Netherlands Organization for Scientific Research NWO. The work of I. Savostianov and W. Hundsdorfer for this publication has been supported by Award No. FIC/2010/05 from the King Abdullah University of Science and Technology (KAUST).
This publication acknowledges KAUST support, but has no KAUST affiliated authors.
PY - 2015/5
Y1 - 2015/5
N2 - © 2014 Elsevier B.V. All rights reserved. One-leg multistep methods have some advantage over linear multistep methods with respect to storage of the past results. In this paper boundedness and monotonicity properties with arbitrary (semi-)norms or convex functionals are analyzed for such multistep methods. The maximal stepsize coefficient for boundedness and monotonicity of a one-leg method is the same as for the associated linear multistep method when arbitrary starting values are considered. It will be shown, however, that combinations of one-leg methods and Runge-Kutta starting procedures may give very different stepsize coefficients for monotonicity than the linear multistep methods with the same starting procedures. Detailed results are presented for explicit two-step methods.
AB - © 2014 Elsevier B.V. All rights reserved. One-leg multistep methods have some advantage over linear multistep methods with respect to storage of the past results. In this paper boundedness and monotonicity properties with arbitrary (semi-)norms or convex functionals are analyzed for such multistep methods. The maximal stepsize coefficient for boundedness and monotonicity of a one-leg method is the same as for the associated linear multistep method when arbitrary starting values are considered. It will be shown, however, that combinations of one-leg methods and Runge-Kutta starting procedures may give very different stepsize coefficients for monotonicity than the linear multistep methods with the same starting procedures. Detailed results are presented for explicit two-step methods.
UR - http://hdl.handle.net/10754/597810
UR - https://linkinghub.elsevier.com/retrieve/pii/S0377042714004737
UR - http://www.scopus.com/inward/record.url?scp=84912557616&partnerID=8YFLogxK
U2 - 10.1016/j.cam.2014.10.025
DO - 10.1016/j.cam.2014.10.025
M3 - Article
SN - 0377-0427
VL - 279
SP - 159
EP - 172
JO - Journal of Computational and Applied Mathematics
JF - Journal of Computational and Applied Mathematics
ER -