@Article{JCM-42-337,
author = {Wang , Wansheng},
title = {Stability and Convergence of Stepsize-Dependent Linear Multistep Methods for Nonlinear Dissipative Evolution Equations in Banach Space },
journal = {Journal of Computational Mathematics},
year = {2024},
volume = {42},
number = {2},
pages = {337--354},
abstract = {<p style="text-align: justify;">Stability and global error bounds are studied for a class of stepsize-dependent linear
multistep methods for nonlinear evolution equations governed by $ω$-dissipative vector fields
in Banach space. To break through the order barrier $p ≤ 1$ of unconditionally contractive
linear multistep methods for dissipative systems, strongly dissipative systems are introduced. By employing the error growth function of the methods, new contractivity and
convergence results of stepsize-dependent linear multistep methods on infinite integration
intervals are provided for strictly dissipative systems $(ω &lt; 0)$ and strongly dissipative systems. Some applications of the main results to several linear multistep methods, including
the trapezoidal rule, are supplied. The theoretical results are also illustrated by a set of
numerical experiments.</p>},
issn = {1991-7139},
doi = {https://doi.org/10.4208/jcm.2207-m2021-0064},
url = {http://global-sci.org/intro/article_detail/jcm/22883.html}
}