Superstable two-step methods for the numerical integration of general second order initial value problems
type: Item
instance of: scholarly article
title: Superstable two-step methods for the numerical integration of general second order initial value problems
zbMATH Open document ID: 0579.65073
DOI: 10.1016/0377-0427(85)90018-4
author: Man M. Chawla
published in: Journal of Computational and Applied Mathematics
publication date: 1985-01-01T00:00:00Z
review text: The paper presents a class of two-step fourth order methods for the numerical integration of the general second order initial value problem. These methods are implicit and need an iterative process at each step. The author proves that the considered methods are superstable for the test equation \(y''+2\alpha y'+\beta^ 2y=0\), \(\alpha,\beta >0\), \(\alpha +\beta >0\). Such a kind of equation occurs, for example, in the numerical integration of singular perturbation problems. In my opinion more studies should be done on the practical application of these new methods. First of all it refers to the comparison of the methods proposed by the author with the other well-known methods for solving the general second order initial value problem. In this paper the author does not present any numerical examples.
Mathematics Subject Classification ID: 65L05
Mathematics Subject Classification ID: 65L20
Mathematics Subject Classification ID: 34A34
zbMATH DE Number: 3928242
zbMATH Keywords: region of absolute stability
zbMATH Keywords: interval of periodicity
zbMATH Keywords: interval of
zbMATH Keywords: weak stability
zbMATH Keywords: superstable methods
zbMATH Keywords: two-step fourth order methods
zbMATH Keywords: second order initial value problem
reviewed by: Andrzej Marciniak
MaRDI profile type: Publication
full work available at URL: 0377-0427(85)90018-4
OpenAlex ID: W2025979560
cites work: Unconditionally stable Noumerov-type methods for second order differential equations
cites work: A Fourth-order Tridiagonal Finite Difference Method for General Non-linear Two-point Boundary Value Problems with Mixed Boundary Conditions
cites work: On accuracy and unconditional stability of linear multistep methods for second order differential equations
cites work: Q3911973
description: scientific article; zbMATH DE number 3928242