Region-dependent optimal \(m\)-stage Runge-Kutta schemes for solving a class of nonsymmetric linear systems
type: Item
instance of: scholarly article
title: Region-dependent optimal \(m\)-stage Runge-Kutta schemes for solving a class of nonsymmetric linear systems
zbMATH Open document ID: 0814.65034
DOI: 10.1016/0024-3795(94)90421-9
author: Chichia Chiu
author: Meiqin Chen
published in: Linear Algebra and its Applications
publication date: 1995-06-18T00:00:00Z
review text: Consider the system of linear algebraic equations \(Ax= b\), where \(A\) is an \(N\times N\) nonsymmetric real matrix with the following properties: (a) The matrix \(A\) is nonsingular and has a complete eigenspace, (b) The real parts of all eigenvalues are nonnegative. The paper presents some analytic and numerical results on \(m\)-stage Runge-Kutta schemes for solving the above system. The solution of the algebraic system is treated as the steady state of a system of ordinary differential equations, \(dx/dy+ Ax= b\). For each \(m\), the authors find a compact complex region \(\Omega\) which has a simply connected complement and contains all eigenvalues of the system. A specially structured nonlinear minimax problem over the region is formulated to find the optimal parameters of the Runge-Kutta method.
Mathematics Subject Classification ID: 65F10
Mathematics Subject Classification ID: 65L06
Mathematics Subject Classification ID: 34A30
zbMATH DE Number: 720494
zbMATH Keywords: nonsymmetric linear systems
zbMATH Keywords: \(m\)-stage Runge-Kutta schemes
zbMATH Keywords: steady state
zbMATH Keywords: system of ordinary differential equations
describes a project that uses: CGS
MaRDI profile type: Publication
full work available at URL: 0024-3795(94)90421-9
OpenAlex ID: W2061560911
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description: scientific article; zbMATH DE number 720494