Stability and Convergence of Stepsize-Dependent Linear Multistep Methods for Nonlinear Dissipative Evolution Equations in Banach Space
Year: 2024
Author: Wansheng Wang
Journal of Computational Mathematics, Vol. 42 (2024), Iss. 2 : pp. 337–354
Abstract
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 $(ω < 0)$ 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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jcm.2207-m2021-0064
Journal of Computational Mathematics, Vol. 42 (2024), Iss. 2 : pp. 337–354
Published online: 2024-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 18
Keywords: Nonlinear evolution equation Linear multistep methods ω-dissipative operators Stability Convergence Banach space.