Additive parameters methods for the numerical integration of \(y''=f(t,y,y')\)
type: Item
instance of: scholarly article
title: Additive parameters methods for the numerical integration of \(y''=f(t,y,y')\)
zbMATH Open document ID: 0861.65061
DOI: 10.1016/0377-0427(94)00127-8
author: A. Sesappa Rai
author: U. Ananthakrishnaiah
published in: Journal of Computational and Applied Mathematics
publication date: 1996-10-13T00:00:00Z
review text: The authors derive a new two step fourth-order method for the numerical integration of the general second-order differential equation \(y''(t)=f(t,y,y')\) subject to the initial conditions \(y(t_0)=y_0\), \(y'(t_0)=y_0'\). The method depends upon the parameters \(p\) and \(q\) which are the new additional values of the coefficients of \(y'\) and \(y\) in the given differential equation. Truncation error and order of the method are reported. It is shown that the method is absolute stable when the parameters are chosen as the coefficients of \(y'\) and \(y\) in the case of a linear differential equation. Numerical results are presented for Bessel's, Legendre's and general second-order differential equations.
Mathematics Subject Classification ID: 65L06
Mathematics Subject Classification ID: 65L20
Mathematics Subject Classification ID: 65L70
Mathematics Subject Classification ID: 34A34
Mathematics Subject Classification ID: 34B30
Mathematics Subject Classification ID: 65L05
zbMATH DE Number: 908373
zbMATH Keywords: additive parameters methods
zbMATH Keywords: absolute stability
zbMATH Keywords: error bound
zbMATH Keywords: numerical examples
zbMATH Keywords: Bessel differential equation
zbMATH Keywords: Legendre differential equation
zbMATH Keywords: two step fourth-order method
zbMATH Keywords: second-order differential equation
reviewed by: Karel Najzar
MaRDI profile type: Publication
full work available at URL: 0377-0427(94)00127-8
OpenAlex ID: W2153890281
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description: scientific article; zbMATH DE number 908373