Extended double-stride \(L\)-stable methods for the numerical solution of ODEs
type: Item
instance of: scholarly article
title: Extended double-stride \(L\)-stable methods for the numerical solution of ODEs
zbMATH Open document ID: 0859.65075
DOI: 10.1016/0898-1221(95)00187-5
author: Man M. Chawla
author: M. S. Al-Sahhar
author: Ahmed Abdullatif Karaballi
publication date: 1997-04-07T00:00:00Z
review text: Two formulae are derived, each of which can be regarded as a modified version of Milne's method. It is claimed that they are both 4th-order and \(L\)-stable. It is proposed to implement these methods for stiff problems by using simple fixed-point iteration, and some numerical results are shown for two scalar test problems. It appears that both methods could be recast as implicit Runge-Kutta methods which would provide a means for checking the results of the paper.
Mathematics Subject Classification ID: 65L06
Mathematics Subject Classification ID: 65L05
Mathematics Subject Classification ID: 34A34
Mathematics Subject Classification ID: 65L20
Mathematics Subject Classification ID: 34E13
zbMATH DE Number: 878516
zbMATH Keywords: multistep methods
zbMATH Keywords: \(L\)-stability
zbMATH Keywords: fourth-order method
zbMATH Keywords: stiff systems
zbMATH Keywords: numerical examples
zbMATH Keywords: Milne's method
zbMATH Keywords: implicit Runge-Kutta methods
MaRDI profile type: Publication
full work available at URL: 0898-1221(95)00187-5
OpenAlex ID: W2011033839
cites work: An \(A\)-stable extended trapezoidal rule for the integration of ordinary differential equations
cites work: Q5674335
cites work: Extended one-step methods for the numerical solution of ordinary differential equations
cites work: Extended a-stable two-step methods for the numerical solution of ordinary differential equations
cites work: A class of stabilized extended one-step methods for the numerical solution of ODEs
cites work: Q3911973
published in: Computers & Mathematics with Applications
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description: scientific article; zbMATH DE number 878516