An improved class of generalized Runge-Kutta methods for stiff problems. I: The scalar case
type: Item
instance of: scholarly article
title: An improved class of generalized Runge-Kutta methods for stiff problems. I: The scalar case
zbMATH Open document ID: 1032.65071
DOI: 10.1016/S0096-3003(01)00115-1
author: Jesús Rojo
author: J. Álvarez
published in: Applied Mathematics and Computation
publication date: 2003-01-28T00:00:00Z
review text: The authors present a new family of \(p\)-stage methods for the numerical integration of some scalar ordinary differential equations (ODEs). The method provides better order and stability results and may be viewed as a generalization of explicit \(p\)-stage Runge-Kutta methods. Explicit \(A\)-stable and \(L\)-stable methods for the numerical integration of scalar autonomous ODEs are obtained at the cost of losing linearity in the formulas. This method is generalized to work for non-autonomous scalar ODEs and systems in a subsequent work. Numerical examples are given to demonstrate the effectiveness of the method.
Mathematics Subject Classification ID: 65L06
Mathematics Subject Classification ID: 65L05
Mathematics Subject Classification ID: 65L20
Mathematics Subject Classification ID: 34A34
zbMATH DE Number: 1861141
zbMATH Keywords: \(p\)-stage methods
zbMATH Keywords: explicit \(p\)-stage Runge-Kutta methods
zbMATH Keywords: stiff systems
zbMATH Keywords: \(A\)-stability
zbMATH Keywords: \(L\)-stability
zbMATH Keywords: order
zbMATH Keywords: numerical examples
describes a project that uses: RODAS
MaRDI profile type: Publication
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full work available at URL: s0096-3003(01)00115-1
OpenAlex ID: W2094733623
description: scientific article; zbMATH DE number 1861141