Accurate Implicit–Explicit General Linear Methods with Inherent Runge–Kutta Stability

Michał Braś, Giuseppe Izzo, Zdzislaw Jackiewicz

Research output: Contribution to journalArticle

13 Citations (Scopus)

Abstract

We investigate implicit–explicit (IMEX) general linear methods (GLMs) with inherent Runge–Kutta stability (IRKS) for differential systems with non-stiff and stiff processes. The construction of such formulas starts with implicit GLMs with IRKS which are A- and L-stable, and then we ‘remove’ implicitness in non-stiff terms by extrapolating unknown stage derivatives by stage derivatives which are already computed by the method. Then we search for IMEX schemes with large regions of absolute stability of the ‘explicit part’ of the method assuming that the ‘implicit part’ of the scheme is (Formula presented.)-stable for some (Formula presented.). Examples of highly stable IMEX GLMs are provided of order (Formula presented.). Numerical examples are also given which illustrate good performance of these schemes.

Original languageEnglish (US)
Pages (from-to)1-39
Number of pages39
JournalJournal of Scientific Computing
DOIs
StateAccepted/In press - Sep 1 2016

Fingerprint

General Linear Methods
Runge-Kutta
Derivatives
Derivative
Absolute Stability
Implicit Method
Differential System
Unknown
Numerical Examples
Term

Keywords

  • Construction of highly stable methods
  • Convergence and stability analysis
  • General linear methods
  • IMEX methods
  • Inherent Runge–Kutta stability

ASJC Scopus subject areas

  • Software
  • Theoretical Computer Science
  • Engineering(all)
  • Computational Theory and Mathematics

Cite this

Accurate Implicit–Explicit General Linear Methods with Inherent Runge–Kutta Stability. / Braś, Michał; Izzo, Giuseppe; Jackiewicz, Zdzislaw.

In: Journal of Scientific Computing, 01.09.2016, p. 1-39.

Research output: Contribution to journalArticle

@article{0b958e80fbf243d08311618a8bfa3d22,
title = "Accurate Implicit–Explicit General Linear Methods with Inherent Runge–Kutta Stability",
abstract = "We investigate implicit–explicit (IMEX) general linear methods (GLMs) with inherent Runge–Kutta stability (IRKS) for differential systems with non-stiff and stiff processes. The construction of such formulas starts with implicit GLMs with IRKS which are A- and L-stable, and then we ‘remove’ implicitness in non-stiff terms by extrapolating unknown stage derivatives by stage derivatives which are already computed by the method. Then we search for IMEX schemes with large regions of absolute stability of the ‘explicit part’ of the method assuming that the ‘implicit part’ of the scheme is (Formula presented.)-stable for some (Formula presented.). Examples of highly stable IMEX GLMs are provided of order (Formula presented.). Numerical examples are also given which illustrate good performance of these schemes.",
keywords = "Construction of highly stable methods, Convergence and stability analysis, General linear methods, IMEX methods, Inherent Runge–Kutta stability",
author = "Michał Braś and Giuseppe Izzo and Zdzislaw Jackiewicz",
year = "2016",
month = "9",
day = "1",
doi = "10.1007/s10915-016-0273-y",
language = "English (US)",
pages = "1--39",
journal = "Journal of Scientific Computing",
issn = "0885-7474",
publisher = "Springer New York",

}

TY - JOUR

T1 - Accurate Implicit–Explicit General Linear Methods with Inherent Runge–Kutta Stability

AU - Braś, Michał

AU - Izzo, Giuseppe

AU - Jackiewicz, Zdzislaw

PY - 2016/9/1

Y1 - 2016/9/1

N2 - We investigate implicit–explicit (IMEX) general linear methods (GLMs) with inherent Runge–Kutta stability (IRKS) for differential systems with non-stiff and stiff processes. The construction of such formulas starts with implicit GLMs with IRKS which are A- and L-stable, and then we ‘remove’ implicitness in non-stiff terms by extrapolating unknown stage derivatives by stage derivatives which are already computed by the method. Then we search for IMEX schemes with large regions of absolute stability of the ‘explicit part’ of the method assuming that the ‘implicit part’ of the scheme is (Formula presented.)-stable for some (Formula presented.). Examples of highly stable IMEX GLMs are provided of order (Formula presented.). Numerical examples are also given which illustrate good performance of these schemes.

AB - We investigate implicit–explicit (IMEX) general linear methods (GLMs) with inherent Runge–Kutta stability (IRKS) for differential systems with non-stiff and stiff processes. The construction of such formulas starts with implicit GLMs with IRKS which are A- and L-stable, and then we ‘remove’ implicitness in non-stiff terms by extrapolating unknown stage derivatives by stage derivatives which are already computed by the method. Then we search for IMEX schemes with large regions of absolute stability of the ‘explicit part’ of the method assuming that the ‘implicit part’ of the scheme is (Formula presented.)-stable for some (Formula presented.). Examples of highly stable IMEX GLMs are provided of order (Formula presented.). Numerical examples are also given which illustrate good performance of these schemes.

KW - Construction of highly stable methods

KW - Convergence and stability analysis

KW - General linear methods

KW - IMEX methods

KW - Inherent Runge–Kutta stability

UR - http://www.scopus.com/inward/record.url?scp=84984831693&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84984831693&partnerID=8YFLogxK

U2 - 10.1007/s10915-016-0273-y

DO - 10.1007/s10915-016-0273-y

M3 - Article

AN - SCOPUS:84984831693

SP - 1

EP - 39

JO - Journal of Scientific Computing

JF - Journal of Scientific Computing

SN - 0885-7474

ER -