The generalized Euler process for exponentially dominant systems
type: Item
instance of: scholarly article
title: The generalized Euler process for exponentially dominant systems
zbMATH Open document ID: 1068.65095
DOI: 10.1016/S0898-1221(04)90014-4
author: Dong Won Yu
publication date: 2004-06-15T00:00:00Z
review text: Generalized Euler and Runge-Kutta algorithms are obtained for a system of exponentially dominant ordinary differential equations \(x'(t)=f(x(t))\), \(t\geq 0\), \(x(t)\in \mathbb R^n\), \(x(0) = x_n\in \mathbb R^n\) by transforming the system by change of dependent variable and applying the algorithms to the transformed system. Let the Jacobian \(J = d/dxf(0)\) be reduced to the real canonical form \(P^{-1}JP =S_0+N_0\), \(S_0\) semisimple and \(N_0\) nilpotent and let \(S=\alpha I+1/2(S_0 - S_0^T)\) where \(\alpha\) is the maximum of the real parts of the eigenvalues of \(J\). The system is transformed to a system in \(z(t) = \exp(- tS)P^{-1}x(t)\). If \(S\neq 0\) the system is exponentially dominant. Results of trials of the new method are compared to results obtained by standard methods, showing the new method to be effective.
Mathematics Subject Classification ID: 65L06
Mathematics Subject Classification ID: 34C20
Mathematics Subject Classification ID: 65L05
Mathematics Subject Classification ID: 34A34
zbMATH DE Number: 2075449
zbMATH Keywords: exponentially dominant system
zbMATH Keywords: real canonical form
zbMATH Keywords: \(s\)-matrix
zbMATH Keywords: \(s\)-transformed system
zbMATH Keywords: generalized Euler process
zbMATH Keywords: logarithmic norm
zbMATH Keywords: contractivity
zbMATH Keywords: Runge-Kutta algorithms
reviewed by: John B. Butler jun.
describes a project that uses: RKSUITE
MaRDI profile type: Publication
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full work available at URL: s0898-1221(04)90014-4
OpenAlex ID: W2083355341
published in: Computers & Mathematics with Applications
description: scientific article; zbMATH DE number 2075449