Erratum to: On the Crank-Nicolson scheme once again
type: Item
instance of: scholarly article
title: Erratum to: On the Crank-Nicolson scheme once again
zbMATH Open document ID: 1239.47034
published in: Journal of Evolution Equations
publication date: 2012-01-13T00:00:00Z
review text: Let \((\tau_j)_{j\in\mathbb{N}}\) be a sequence of strictly positive real numbers, and let \(A\) be the generator of a bounded analytic semigroup in a Banach space \(X\). Put \(A_n=\prod_{j=1}^n(I+\frac{1}{2}\tau_jA)(I-\frac{1}{2}\tau_jA)^{-1}\), and let \(x\in X\). Define the sequence \((x_n)_{n\in\mathbb{N}}\subset X\) by the Crank-Nicolson scheme: \(x_n = A_n x\). In a previous paper [``On the Crank-Nicolson scheme once again'', J. Evol. Equ. 11, No. 2, 457--476 (2011; Zbl 1239.47035)], the author made a serious flaw that affects the main stability result. In this Erratum, the author gives the correct formulation and proves that the Crank-Nicolson scheme is stable in the sense that \(\sup_{n\in\mathbb{N}}\| A_nx\| < \infty\), provided that a suitable inequality holds.
reviewed by: Vincenzo Vespri
Mathematics Subject Classification ID: 47D06
Mathematics Subject Classification ID: 34G10
Mathematics Subject Classification ID: 34K30
Mathematics Subject Classification ID: 65J10
zbMATH DE Number: 5997673
zbMATH Keywords: Crank-Nicolson scheme
zbMATH Keywords: bounded analytic semigroup
zbMATH Keywords: numerical methods
author: J. Van Casteren
MaRDI profile type: Publication
full work available at URL: s00028-011-0108-0
OpenAlex ID: W2059043418
cites work: On the Crank-Nicolson scheme once again
DOI: 10.1007/S00028-011-0108-0
description: scientific article; zbMATH DE number 5997673