Stability and Convergence of Stepsize-Dependent Linear Multistep Methods for Nonlinear Dissipative Evolution Equations in Banach Space

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.

Author Details

Wansheng Wang