Generalized linear multistep methods for ordinary differential equations

Giuseppe Izzo; Zdzislaw Jackiewicz

doi:10.1016/j.apnum.2016.04.009

Generalized linear multistep methods for ordinary differential equations

Giuseppe Izzo, Zdzislaw Jackiewicz

Mathematical and Statistical Sciences, School of (SoMSS)

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

8 Scopus citations

Abstract

In this paper we use the theoretical framework of General Linear Methods (GLMs) to analyze and generalize the class of Cash's Modified Extended Backward Differentiation Formulae (MEBDF). Keeping the structure of MEBDF and their computational cost we propose a more general class of methods that can be viewed as a composition of modified linear multistep methods. These new methods are characterized by smaller error constants and possibly larger angles of A(α)-stability. Numerical experiments which confirm the good performance of these methods on a set of stiff problems are also reported.

Original language	English (US)
Pages (from-to)	165-178
Number of pages	14
Journal	Applied Numerical Mathematics
Volume	114
DOIs	https://doi.org/10.1016/j.apnum.2016.04.009
State	Published - Apr 1 2017

Keywords

A(α)-stability
A-stability
Error constants
Extended Backward Differentiation Formulae
L(α)-stability
L-stability
MEBDF
PMEBDF
Stiff problems

ASJC Scopus subject areas

Numerical Analysis
Computational Mathematics
Applied Mathematics

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10.1016/j.apnum.2016.04.009

Cite this

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title = "Generalized linear multistep methods for ordinary differential equations",

abstract = "In this paper we use the theoretical framework of General Linear Methods (GLMs) to analyze and generalize the class of Cash's Modified Extended Backward Differentiation Formulae (MEBDF). Keeping the structure of MEBDF and their computational cost we propose a more general class of methods that can be viewed as a composition of modified linear multistep methods. These new methods are characterized by smaller error constants and possibly larger angles of A(α)-stability. Numerical experiments which confirm the good performance of these methods on a set of stiff problems are also reported.",

keywords = "A(α)-stability, A-stability, Error constants, Extended Backward Differentiation Formulae, L(α)-stability, L-stability, MEBDF, PMEBDF, Stiff problems",

author = "Giuseppe Izzo and Zdzislaw Jackiewicz",

note = "Funding Information: The work of the first author (GI) was partially supported by the research project “Analysis of complex biological systems” of the Department of Mathematics and Applications at University of Napoli “Federico II” , Napoli, Italy. Publisher Copyright: {\textcopyright} 2016 IMACS",

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AU - Izzo, Giuseppe

AU - Jackiewicz, Zdzislaw

N1 - Funding Information: The work of the first author (GI) was partially supported by the research project “Analysis of complex biological systems” of the Department of Mathematics and Applications at University of Napoli “Federico II” , Napoli, Italy. Publisher Copyright: © 2016 IMACS

PY - 2017/4/1

Y1 - 2017/4/1

N2 - In this paper we use the theoretical framework of General Linear Methods (GLMs) to analyze and generalize the class of Cash's Modified Extended Backward Differentiation Formulae (MEBDF). Keeping the structure of MEBDF and their computational cost we propose a more general class of methods that can be viewed as a composition of modified linear multistep methods. These new methods are characterized by smaller error constants and possibly larger angles of A(α)-stability. Numerical experiments which confirm the good performance of these methods on a set of stiff problems are also reported.

AB - In this paper we use the theoretical framework of General Linear Methods (GLMs) to analyze and generalize the class of Cash's Modified Extended Backward Differentiation Formulae (MEBDF). Keeping the structure of MEBDF and their computational cost we propose a more general class of methods that can be viewed as a composition of modified linear multistep methods. These new methods are characterized by smaller error constants and possibly larger angles of A(α)-stability. Numerical experiments which confirm the good performance of these methods on a set of stiff problems are also reported.

KW - A(α)-stability

KW - A-stability

KW - Error constants

KW - Extended Backward Differentiation Formulae

KW - L(α)-stability

KW - L-stability

KW - MEBDF

KW - PMEBDF

KW - Stiff problems

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DO - 10.1016/j.apnum.2016.04.009

M3 - Article

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SN - 0168-9274

VL - 114

SP - 165

EP - 178

JO - Applied Numerical Mathematics

JF - Applied Numerical Mathematics

ER -

Generalized linear multistep methods for ordinary differential equations

Abstract

Keywords

ASJC Scopus subject areas

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