General linear methods for \(y^{\prime\prime} = f(y(t))\)
type: Item
instance of: scholarly article
title: General linear methods for \(y^{\prime\prime} = f(y(t))\)
zbMATH Open document ID: 1275.65039
published in: Numerical Algorithms
publication date: 2012-12-21T00:00:00Z
review text: The paper introduces a general family of numerical methods which are more convenient to numerically integrating initial value problems based on special second-order ordinary differential equations of the form \[ \begin{cases} y''(t) = f(y(t)), \quad t\in [t_0, T], \\ y(t_0)= y_0 \in \mathbb{R}^d, \\ y'(t_0)= y'_0 \in \mathbb{R}^d, \end{cases} \] where the function \( f: \mathbb{R}^d \rightarrow \mathbb{R}^d \) does not explicitly depend on \( y' \) and is supposed to be smooth enough to guarantee that the problem is Hadamard well-posed. Consistency, zero-stability and convergence of the solutions of the problem are studied. The paper is mainly focused on the development of a unifying framework for the numerical solutions of special-order ordinary differential equations by considering the family of general linear methods.
Mathematics Subject Classification ID: 65L05
Mathematics Subject Classification ID: 34A34
Mathematics Subject Classification ID: 65L20
zbMATH DE Number: 6117970
zbMATH Keywords: second-order ordinary differential equations
zbMATH Keywords: general linear methods
zbMATH Keywords: convergence analysis
zbMATH Keywords: initial value problem
zbMATH Keywords: consistency
zbMATH Keywords: zero-stability
author: Raffaele D'Ambrosio
author: Elena Esposito
author: Beatrice Paternoster
reviewed by: Haydar Akca
describes a project that uses: RODAS
MaRDI profile type: Publication
full work available at URL: s11075-012-9637-z
OpenAlex ID: W2123271762
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DOI: 10.1007/S11075-012-9637-Z
description: scientific article; zbMATH DE number 6117970