Singly-implicit Runge-Kutta methods for retarded and ordinary differential equations
type: Item
instance of: scholarly article
title: Singly-implicit Runge-Kutta methods for retarded and ordinary differential equations
zbMATH Open document ID: 0695.65047
DOI: 10.1007/BF02242918
author: H. Claus
published in: Computing
publication date: 1990-01-01T00:00:00Z
review text: Singly implicit Runge-Kutta methods (i.e., methods whose Runge-Kutta matrix has only one real eigenvalue of multiplicity s) are reviewed. Their suitability for the numerical solution of stiff delay differential equations is promoted, and two new codes are presented together with several numerical experiments. This article contains an interesting characterization of the P-stability region (with respect to \(y'(t)=ay(t)+by(t-\tau)\), \(a,b\in C\), \(\tau >0)\) for general numerical procedures.
Mathematics Subject Classification ID: 65L05
Mathematics Subject Classification ID: 65L20
Mathematics Subject Classification ID: 34K05
zbMATH DE Number: 4139219
zbMATH Keywords: Singly implicit Runge-Kutta methods
zbMATH Keywords: stiff delay differential equations
zbMATH Keywords: numerical experiments
zbMATH Keywords: P-stability region
reviewed by: Ernst Hairer
MaRDI profile type: Publication
cites work: Numerical solution of retarded initial value problems: Local and global error and stepsize control
cites work: Special stability problems for functional differential equations
cites work: On the computational solution of differential-difference equations
cites work: A special family of Runge-Kutta methods for solving stiff differential equations
cites work: An implementation of singly-implicit Runge-Kutta methods
cites work: On the implementation of implicit Runge-Kutta methods
cites work: A Transformed implicit Runge-Kutta Method
cites work: Partitioned adaptive Runge-Kutta methods for the solution of nonstiff and stiff systems
cites work: Comparing numerical methods for stiff systems of O.D.E:s
cites work: A reliable Rosenbrock integrator for stiff differential equations
cites work: Q3779682
cites work: Fourth- and Fifth-Order, Scaled Rungs–Kutta Algorithms for Treating Dense Output
cites work: Local error control in SDIRK-methods
cites work: Numerical treatment of delay differential equations by Hermite interpolation
cites work: Interpolation for Runge–Kutta Methods
cites work: Q5610717
cites work: Stability Analysis of Linearly Implicit One-Step Interpolation Methods for Stiff Retarded Differential Equations
cites work: The Stability of Difference Formulas for Delay Differential Equations
cites work: A type insensitive code for delay differential equations basing on adaptive and explicit Runge-Kutta interpolation methods
cites work: One-Step Collocation: Uniform Superconvergence, Predictor-Corrector Method, Local Error Estimate
cites work: Natural Continuous Extensions of Runge-Kutta Methods
full work available at URL: https://doi.org/10.1007/bf02242918
OpenAlex ID: W181177096
description: scientific article; zbMATH DE number 4139219