Construction of highly stable parallel two-step Runge-Kutta methods for delay differential equations

Z. Bartoszewski; Zdzislaw Jackiewicz

doi:10.1016/j.cam.2007.08.007

Construction of highly stable parallel two-step Runge-Kutta methods for delay differential equations

Z. Bartoszewski, Zdzislaw Jackiewicz

CLAS-NS: Mathematical and Statistical Sciences, School of (SMSS)

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

Abstract

It is shown that any A-stable two-step Runge-Kutta method of order over(p, ̃) and stage order q = over(p, ̃) for ordinary differential equations can be extended to the P-stable method of uniform order p = over(p, ̃) for delay differential equations.

Original language	English (US)
Pages (from-to)	257-270
Number of pages	14
Journal	Journal of Computational and Applied Mathematics
Volume	220
Issue number	1-2
DOIs	https://doi.org/10.1016/j.cam.2007.08.007
State	Published - Oct 15 2008

Keywords

A-stability
Delay differential equations
P-stability
Two-step Runge-Kutta methods
Uniform convergence

ASJC Scopus subject areas

Computational Mathematics
Applied Mathematics

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10.1016/j.cam.2007.08.007

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title = "Construction of highly stable parallel two-step Runge-Kutta methods for delay differential equations",

abstract = "It is shown that any A-stable two-step Runge-Kutta method of order over(p,{\~ }) and stage order q = over(p,{\~ }) for ordinary differential equations can be extended to the P-stable method of uniform order p = over(p,{\~ }) for delay differential equations.",

keywords = "A-stability, Delay differential equations, P-stability, Two-step Runge-Kutta methods, Uniform convergence",

author = "Z. Bartoszewski and Zdzislaw Jackiewicz",

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AU - Jackiewicz, Zdzislaw

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N2 - It is shown that any A-stable two-step Runge-Kutta method of order over(p, ̃) and stage order q = over(p, ̃) for ordinary differential equations can be extended to the P-stable method of uniform order p = over(p, ̃) for delay differential equations.

AB - It is shown that any A-stable two-step Runge-Kutta method of order over(p, ̃) and stage order q = over(p, ̃) for ordinary differential equations can be extended to the P-stable method of uniform order p = over(p, ̃) for delay differential equations.

KW - A-stability

KW - Delay differential equations

KW - P-stability

KW - Two-step Runge-Kutta methods

KW - Uniform convergence

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M3 - Article

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JO - Journal of Computational and Applied Mathematics

JF - Journal of Computational and Applied Mathematics

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IS - 1-2

ER -

Construction of highly stable parallel two-step Runge-Kutta methods for delay differential equations

Abstract

Keywords

ASJC Scopus subject areas

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