The energy technique for the six-step BDF method
Numerical Analysis
2020-07-20 v1 Numerical Analysis
Abstract
In combination with the Grenander--Szeg\"o theorem, we observe that a relaxed positivity condition on multipliers, milder than the basic %fundamental requirement of the Nevanlinna--Odeh multipliers that the sum of the absolute values of their components is strictly less than , makes the energy technique applicable to the stability analysis of BDF methods for parabolic equations with selfadjoint elliptic part. This is particularly useful for the six-step BDF method for which no Nevanlinna--Odeh multiplier exists. We introduce multipliers satisfying the positivity property for the six-step BDF method and establish stability of the method for parabolic equations.
Cite
@article{arxiv.2007.08924,
title = {The energy technique for the six-step BDF method},
author = {Georgios Akrivis and Minghua Chen and Fan Yu and Zhi Zhou},
journal= {arXiv preprint arXiv:2007.08924},
year = {2020}
}
Comments
15 pages