Construction of highly stable two-step W-methods for ordinary differential equations

Zdzislaw Jackiewicz; H. Podhaisky; R. Weiner

doi:10.1016/j.cam.2003.10.007

Construction of highly stable two-step W-methods for ordinary differential equations

Zdzislaw Jackiewicz, H. Podhaisky, R. Weiner

Mathematical and Statistical Sciences, School of (SoMSS)

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

11 Scopus citations

Abstract

We describe the construction of linearly implicit two-step W-methods of high stage order and desirable stability properties for the numerical solution of stiff differential systems. The presented methods are demonstrated to be A- and L-stable when the stepsize is held constant. They also preserve good stability properties in a variable stepsize environment under quite demanding conditions imposed on the stepsize pattern.

Original language	English (US)
Pages (from-to)	389-403
Number of pages	15
Journal	Journal of Computational and Applied Mathematics
Volume	167
Issue number	2
DOIs	https://doi.org/10.1016/j.cam.2003.10.007
State	Published - Jun 1 2004

Keywords

A-stability
L-stability
Stiff differential systems
Two-step W-methods

ASJC Scopus subject areas

Computational Mathematics
Applied Mathematics

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10.1016/j.cam.2003.10.007

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title = "Construction of highly stable two-step W-methods for ordinary differential equations",

abstract = "We describe the construction of linearly implicit two-step W-methods of high stage order and desirable stability properties for the numerical solution of stiff differential systems. The presented methods are demonstrated to be A- and L-stable when the stepsize is held constant. They also preserve good stability properties in a variable stepsize environment under quite demanding conditions imposed on the stepsize pattern.",

keywords = "A-stability, L-stability, Stiff differential systems, Two-step W-methods",

author = "Zdzislaw Jackiewicz and H. Podhaisky and R. Weiner",

note = "Funding Information: The authors wish to express their gratitude to anonymous referees for useful comments. The work of Z.J. was partially supported by the National Science Foundation under grant NSF DMS-9971164.",

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T1 - Construction of highly stable two-step W-methods for ordinary differential equations

AU - Jackiewicz, Zdzislaw

AU - Podhaisky, H.

AU - Weiner, R.

N1 - Funding Information: The authors wish to express their gratitude to anonymous referees for useful comments. The work of Z.J. was partially supported by the National Science Foundation under grant NSF DMS-9971164.

PY - 2004/6/1

Y1 - 2004/6/1

N2 - We describe the construction of linearly implicit two-step W-methods of high stage order and desirable stability properties for the numerical solution of stiff differential systems. The presented methods are demonstrated to be A- and L-stable when the stepsize is held constant. They also preserve good stability properties in a variable stepsize environment under quite demanding conditions imposed on the stepsize pattern.

AB - We describe the construction of linearly implicit two-step W-methods of high stage order and desirable stability properties for the numerical solution of stiff differential systems. The presented methods are demonstrated to be A- and L-stable when the stepsize is held constant. They also preserve good stability properties in a variable stepsize environment under quite demanding conditions imposed on the stepsize pattern.

KW - A-stability

KW - L-stability

KW - Stiff differential systems

KW - Two-step W-methods

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DO - 10.1016/j.cam.2003.10.007

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VL - 167

SP - 389

EP - 403

JO - Journal of Computational and Applied Mathematics

JF - Journal of Computational and Applied Mathematics

IS - 2

ER -

Construction of highly stable two-step W-methods for ordinary differential equations

Abstract

Keywords

ASJC Scopus subject areas

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