Generalized linear multistep methods for ordinary differential equations

Giuseppe Izzo, Zdzislaw Jackiewicz

Research output: Contribution to journalArticle

2 Citations (Scopus)

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 languageEnglish (US)
JournalApplied Numerical Mathematics
DOIs
StateAccepted/In press - 2016

Fingerprint

Linear multistep Methods
Ordinary differential equations
Backward Differentiation Formula
Ordinary differential equation
Chemical analysis
General Linear Methods
Stiff Problems
Costs
Experiments
Computational Cost
Numerical Experiment
Angle
Generalise
Class

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

  • Applied Mathematics
  • Computational Mathematics
  • Numerical Analysis

Cite this

@article{1771f036be844ed4aa984b4c2e0146d5,
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",
year = "2016",
doi = "10.1016/j.apnum.2016.04.009",
language = "English (US)",
journal = "Applied Numerical Mathematics",
issn = "0168-9274",
publisher = "Elsevier",

}

TY - JOUR

T1 - Generalized linear multistep methods for ordinary differential equations

AU - Izzo, Giuseppe

AU - Jackiewicz, Zdzislaw

PY - 2016

Y1 - 2016

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

UR - http://www.scopus.com/inward/record.url?scp=84964780732&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84964780732&partnerID=8YFLogxK

U2 - 10.1016/j.apnum.2016.04.009

DO - 10.1016/j.apnum.2016.04.009

M3 - Article

AN - SCOPUS:84964780732

JO - Applied Numerical Mathematics

JF - Applied Numerical Mathematics

SN - 0168-9274

ER -