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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

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Strong-stability-preserving additive linear multistep methods
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by Yiannis Hadjimichael and David I. Ketcheson PDF
Math. Comp. 87 (2018), 2295-2320 Request permission

Abstract:

The analysis of strong-stability-preserving (SSP) linear multistep methods is extended to semi-discretized problems for which different terms on the right-hand side satisfy different forward Euler (or circle) conditions. Optimal perturbed and additive monotonicity-preserving linear multistep methods are studied in the context of such problems. Optimal perturbed methods attain larger monotonicity-preserving step sizes when the different forward Euler conditions are taken into account. On the other hand, we show that optimal SSP additive methods achieve a monotonicity-preserving step-size restriction no better than that of the corresponding nonadditive SSP linear multistep methods.
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Additional Information
  • Yiannis Hadjimichael
  • Affiliation: 4700 King Abdullah University of Science and Technology (KAUST), Thuwal, 23955-6900, Saudi Arabia
  • Address at time of publication: Eötvös Loránd University, MTA-ELTE Numerical Analysis and Large Networks Research Group, Pázmány Péter sétány 1/C, Budapest H-1117, Hungary; and Budapest University of Technology and Economics, Department of Differential Equations, Building H, Egry József utca 1, Budapest H-1111, Hungary
  • MR Author ID: 1029413
  • Email: hadjimy@cs.elte.hu
  • David I. Ketcheson
  • Affiliation: 4700 King Abdullah University of Science and Technology (KAUST), Thuwal, 23955-6900, Saudi Arabia.
  • Email: david.ketcheson@kaust.edu.sa
  • Received by editor(s): April 5, 2016
  • Received by editor(s) in revised form: December 6, 2016, and April 18, 2017
  • Published electronically: February 20, 2018
  • Additional Notes: This work was supported by the King Abdullah University of Science and Technology (KAUST), 4700 Thuwal, 23955-6900, Saudi Arabia
  • © Copyright 2018 American Mathematical Society
  • Journal: Math. Comp. 87 (2018), 2295-2320
  • MSC (2010): Primary 65L06; Secondary 65L05, 65M20
  • DOI: https://doi.org/10.1090/mcom/3296
  • MathSciNet review: 3802436