TY - JOUR
T1 - Stability and Convergence of Stepsize-Dependent Linear Multistep Methods for Nonlinear Dissipative Evolution Equations in Banach Space 
AU - Wang , Wansheng
JO - Journal of Computational Mathematics
VL - 2
SP - 337
EP - 354
PY - 2024
DA - 2024/01
SN - 42
DO - http://doi.org/10.4208/jcm.2207-m2021-0064
UR - https://global-sci.org/intro/article_detail/jcm/22883.html
KW - Nonlinear evolution equation, Linear multistep methods, ω-dissipative operators, Stability, Convergence, Banach space.
AB - <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>