Continuous two-step Runge-Kutta methods for ordinary differential equations
type: Item
instance of: scholarly article
title: Continuous two-step Runge-Kutta methods for ordinary differential equations
zbMATH Open document ID: 1191.65092
author: Raffaele D'Ambrosio
author: Zdzislaw Jackiewicz
published in: Numerical Algorithms
publication date: 2010-05-26T00:00:00Z
review text: The authors develop continuous \(A\)-stable and \(L\)-stable two-step Runge-Kutta methods using some interpolation and collocation conditions for the solution of initial value problems. They also obtain conditions to obtain Runge-Kutta stability. Numerical results are given to support the proposed methods.
Mathematics Subject Classification ID: 65L06
Mathematics Subject Classification ID: 65L20
Mathematics Subject Classification ID: 65L05
Mathematics Subject Classification ID: 34A34
zbMATH DE Number: 5712403
zbMATH Keywords: two-step collocation methods
zbMATH Keywords: \(A\)-stability
zbMATH Keywords: \(L\)-stability
zbMATH Keywords: quadratic stability functions
zbMATH Keywords: Runge-Kutta stability
zbMATH Keywords: two-step Runge-Kutta methods
zbMATH Keywords: initial value problems
zbMATH Keywords: numerical results
describes a project that uses: RODAS
MaRDI profile type: Publication
full work available at URL: s11075-009-9329-5
OpenAlex ID: W1972988100
cites work: Construction of two-step Runge-Kutta methods of high order of ordinary differential equations
cites work: Stability analysis of two-step Runge-Kutta methods for delay differential equations
cites work: Nordsieck representation of two-step Runge-Kutta methods for ordinary differential equations
cites work: Derivation of continuous explicit two-step Runge-Kutta methods of order three
cites work: Construction of highly stable parallel two-step Runge-Kutta methods for delay differential equations
cites work: Q4725642
cites work: Numerical Methods for Ordinary Differential Equations
cites work: Order conditions for two-step Runge-Kutta methods
cites work: Construction of two-step Runge--Kutta methods with large regions of absolute stability
cites work: Two-step almost collocation methods for Volterra integral equations
cites work: Two-step almost collocation methods for ordinary differential equations
cites work: Collocation–Based Two Step Runge–Kutta Methods for Ordinary Differential Equations
cites work: Order Conditions for General Two-Step Runge--Kutta Methods
cites work: Q4714145
cites work: Q3562881
cites work: A General Class of Two-Step Runge–Kutta Methods for Ordinary Differential Equations
cites work: Variable stepsize continuous two-step Runge-Kutta methods for ordinary differential equations
cites work: Derivation and implementation of two-step Runge-Kutta pairs
cites work: Q5674335
cites work: Superconvergence for Multistep Collocation
cites work: On the Stability and Accuracy of One-Step Methods for Solving Stiff Systems of Ordinary Differential Equations
cites work: Implementation of two-step Runge-Kutta methods for ordinary differential equations
cites work: Two-step Runge-Kutta: Theory and practice
DOI: 10.1007/S11075-009-9329-5
description: scientific article; zbMATH DE number 5712403