An AN-stable Rosenbrock-type method for solving stiff differential equations
type: Item
instance of: scholarly article
title: An AN-stable Rosenbrock-type method for solving stiff differential equations
zbMATH Open document ID: 0621.65070
DOI: 10.1016/0898-1221(87)90122-2
publication date: 1987-01-01T00:00:00Z
review text: For the equation \(y'=\lambda (x)y\) the stability properties of Rosenbrock-Wanner (ROW) methods are investigated. It is shown that k- stage ROW-methods are not AN-stable for \(k\geq 2\). A second order improved ROW-method, which is AN-stable and with local error estimate is presented with some numerical results. The method is needed to be tested over a wide range of problems; the local truncation error must be estimated efficiently.
reviewed by: Edmond V. Nicolau
Mathematics Subject Classification ID: 65L05
Mathematics Subject Classification ID: 65L20
Mathematics Subject Classification ID: 34A30
zbMATH DE Number: 4007614
zbMATH Keywords: Rosenbrock-Wanner methods
zbMATH Keywords: numerical example
zbMATH Keywords: AN-stability
zbMATH Keywords: local error estimate
zbMATH Keywords: local truncation error
author: Hussein Zedan
MaRDI profile type: Publication
full work available at URL: 0898-1221(87)90122-2
OpenAlex ID: W2025125977
cites work: Some general implicit processes for the numerical solution of differential equations
cites work: Generalized Runge-Kutta methods of order four with stepsize control for stiff ordinary differential equations
cites work: A study of Rosenbrock-type methods of high order
cites work: Stability Criteria for Implicit Runge–Kutta Methods
published in: Computers & Mathematics with Applications
description: scientific article; zbMATH DE number 4007614