Highly stable parallel Volterra Runge-Kutta methods
type: Item
instance of: scholarly article
title: Highly stable parallel Volterra Runge-Kutta methods
zbMATH Open document ID: 0856.65144
DOI: 10.1016/0377-0427(95)00235-9
published in: Journal of Computational and Applied Mathematics
publication date: 1997-02-24T00:00:00Z
review text: A new family of parallel \(V\)-stable methods for second kind Volterra integral equations are investigated. In the author's previous works, the parallel iterated Volterra Runge-Kutta (PIVRK) method and the transformed Volterra Runge-Kutta method (TVRK) have been introduced [cf. \textit{E. Crisci}, \textit{E. Russo}, \textit{P. J. Van der Houwen} and \textit{A. Vecchio}, J. Comput. Appl. Math. 45, No. 1-2, 169-180 (1993; Zbl 0802.65133)]. In this paper a parallel method having better stability characteristics than the above-mentioned PIVRK and less cost than the TVRK methods is constructed. The new method, called PTVRK (parallel transformed Volterra Runge-Kutta) method is \(V\)-stable. Many particular methods of order \(p\) ranging from 2 to 8 are listed. In the end, numerical experiments are performed.
Mathematics Subject Classification ID: 65R20
Mathematics Subject Classification ID: 45D05
Mathematics Subject Classification ID: 65Y05
zbMATH DE Number: 910313
zbMATH Keywords: parallel computation
zbMATH Keywords: parallel iterated Volterra Runge-Kutta method
zbMATH Keywords: second kind Volterra integral equations
zbMATH Keywords: transformed Volterra Runge-Kutta method
zbMATH Keywords: stability
zbMATH Keywords: numerical experiments
author: Antonia Vecchio
reviewed by: Iulian Coroian
MaRDI profile type: Publication
full work available at URL: 0377-0427(95)00235-9
OpenAlex ID: W2044667037
cites work: Stability Analysis of Runge-Kutta Methods for Volterra Integral Equations of the Second Kind
cites work: Q3875281
cites work: Q3750978
cites work: Stability of parallel Volterra-Runge-Kutta methods
cites work: A class of parallel \(V_0\)-stable methods for Volterra integral equations
cites work: Q4692887
cites work: Q3696472
cites work: Numerical methods for Volterra equations of the second kind
cites work: Lectures on viscoelasticity theory
cites work: Iterated Runge–Kutta Methods on Parallel Computers
cites work: Embedded Diagonally Implicit Runge-Kutta Algorithms on Parallel Computers
cites work: Backward differentiation type formulas for Volterra integral equations of the second kind
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description: scientific article; zbMATH DE number 910313